# Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids

The Volume and Similar Solids of Chapter of this Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids help the students learn the essential lessons associated with the volume. By using Big Ideas Math Answers Grade 8 Chapter 10 Volume and Similar Solids, you can understand the topics of all the chapters easily. Thus the students who wish to prepare Grade 8 concepts can get a strong foundation by accessing our Big Ideas Math Book 8th Grade Answer Key Chapter 10 Volume and Similar Solids.

## Big Ideas Math Book 8th Grade Answer Key Chapter 10 Volume and Similar Solids

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Lesson: 1 Volumes of Cylinders

Lesson: 2 Volumes of Cones

Lesson: 3 Volumes of Spheres

Lesson: 4 Surface Areas and Volumes of Similar Solids

Chapter: 10 – Volume and Similar Solids

### Volume and Similar Solids STEAM Video/Performance Task

STEAM Video

Canning Salsa
You can estimate the volumes of ingredients to predict the total volume of a finished recipe. In what other real-life situations is it helpful to know the volumes of objects?

Watch the STEAM Video “Canning Salsa.” Then answer the following questions.
1. You can approximate the volumes of foods by comparing them to common solids. A cube of cheese has side lengths of 3 centimeters. What is the volume of the cheese?
2. The table shows the amounts x (in cubic inches) of tomato used to make y cubic inches of salsa.

a. Is there a proportional relationship between x and y? Justify your answer.
b. How much tomato do you need to make 15 cubic inches of salsa?

1. The volume of the cheese = 27 cubic centimeters.
2. a = 1: 3 relationship.
b. 5 tomatoes are used to make 15 cubic inches of salsa.

Explanation:
1. Given that a cube of cheese has a side length of 3 centimeters.
the volume of cube = s³
volume = side x side x side
volume = 3 x 3 x 3
volume = 27 cubic centimeters.
2. The relationship given in the above table is a 1: 3  ratio.
1 x 3 = 3
2 x 3 = 6
3 x 3 = 9
4 x 3 = 12.
b. The tomatoes  used to make 15 cubic inches of salsa = 5
5 x 3 = 15

Packaging Salsa
After completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given the dimensions of a jar and a shipping box.

You will be asked questions about how to package jars of salsa. Why is it helpful to know how many jars of salsa fit in one box?

### Volume and Similar Solids Getting Ready for Chapter 10

Chapter Exploration
1. Work with a partner.

a. How does the volume of the stack of dimes compare to the volume of a single dime?
b. How does the volume of the stack of nickels compare to the volume of the stack of dimes? Explain your reasoning. (The height of each stack is identical.)
c. How does the volume of each stack change when you double the number of coins?
d. LOGIC Your friend adds coins to both stacks so that the volume of the stack of dimes is greater than the volume of the stack of nickels. What can you conclude about the number of coins added to each stack? Explain your reasoning.

Vocabulary

The following vocabulary terms are defined in this chapter. Think about what each term might mean and record your thoughts.
cone
hemisphere
sphere
similar solids

cone = A solid or hollow object which tapers from a circular or roughly circular base to a point.
hemisphere = a half of the celestial sphere as divided into two halves by the horizon.
sphere = a round solid figure, or its surface, with every point on its surface equidistant from its center.
similar solids = two solids are similar if they are the same type of solid and their corresponding radii, heights, base lengths, widths, etc. are proportional.

### Lesson 10.1 Volumes of Cylinders

EXPLORATION 1

Exploring Volume
Work with a partner.
a. Each prism shown has a height of h units and bases with areas of B square units. Write a formula that you can use to find the volume of each prism.

b. How can you find the volume of a prism with bases that each have 100 sides?
c. Make a conjecture about how to find the volume of a cylinder. Explain your reasoning.

a. Volume of triangular prism = (bhl/2)
rectangular prism = lwh
pentagonal prism =(1/2)(5 s x a) h
Hexagonal prism = BH
octagonal prism = (A x H)/2
b. volume of prism = 5,00,000
c. volume of cylinder = πr² h

Explanation:
a. volume of traingular prism = (bhl/2)
where b = base, h = height, l= length.
rectangular prism = lwh
where l = length, w= width, h= height.
pentagonal prism = (1/2) x (5 s x a) h
where s = side , a= area , h= height.
hexagonal prism = BH
where b = base h = height
octagonal prism = (A X H)/2
A = area , H = height
volume of triangular prism = (bhl/2)
volume = (100 x 100 x 100/2)
volume = (100x 100 x 50)
volume = 5,00,000
volume of cylinder =πr² h
where r = radius and h = height.

EXPLORATION 2

Finding Volume Experimentally
Work with a partner. Draw a net for a cylinder. Then cut out the net and use tape to form an open cylinder. Repeat this process to form an open cube. The edge length of the cube should be greater than the diameter and the height of the cylinder.

a.Use your conjecture in Exploration 1 to find the volume of the cylinder.
b. Fill the cylinder with rice. Then pour the rice into the open cube. Find the volume of rice in the cube. Does this support your answer in part(a)? Explain your reasoning.

a. volume of cylinder = πr² h
b. we did not find the volume of rice in the cube.

Explanation:
a. volume of cylinder  = πr² h
where r = radius , h = height
b. we did not find the volume of rice in the cube because they did not give the value for the volume of rice.

Try It

Question 1.
Find the volume of a cylinder with a radius of 4 feet and a height of 15 feet. Round your answer to the nearest tenth.

volume of cylinder =  753.6 cubic feet.

Explanation:
volume of cylinder =πr² h
where r = radius and h = height.
r = 4 feet , h = 15 feet π = 3.14 given.
v = π x 4 x 4 x 15
v = 3.14 x 16 x 15
v = 753.6 cubic feet.

Question 2.
Find the height of the cylinder at the left. Round your answer to the nearest tenth.

height of the cylinder =0.28545 cm

Explanation:
volume of cylinder =πr² h
where r = radius and h = height.
r = 4 cm , v = 176  π = 3.14 given.
176= π x 4  x 4 x h
176= 3.14 x 16 h
176 = 50.24 h
h = (50.24/176)
h = 0.28545 cm

Question 3.

radius of the cylinder = 0.2242 m²

Explanation:
volume of cylinder =πr² h
where r = radius and h = height.
h = 4 m , v = 28  π = 3.14 given.
28= π x r  x r x 4
28= 3.14 x 4 r²
28 = 12.56 r²
r² = (12.56/28)
r² = 0.44857143 m⁴
r = 0.2242 m²

Question 4.

radius of the cylinder =0.01183067 mm²

Explanation:
volume of cylinder =πr² h
where r = radius and h = height.
h = 4.25mm , v = 564  π = 3.14 given.
564= π x r  x r x 4.25
564= 3.14 x 4.25 r²
564= 13.345 r²
r² = (13.345/564)
r² = 0.02366135.
r = 0.01183067 mm²

Self-Assessment for Concepts & Skills
Solve each exercise. Then rate your understanding of the success criteria in your journal.

Question 5.
FINDING THE VOLUME OF A CYLINDER
Find the volume of the cylinder at the left. Round your answer to the nearest tenth.

volume of cylinder = 43.96 cu yds

Explanation:
volume of cylinder = πr² h
where π = 3.14  diameter = 4 given
r = (4/2)
r = 2 , h = 3.5
v = 3.14 x 2 x 2 x 3.5
v = 6.28 x 2 x 3.5
v = 12.56 x 3.5
v = 43.96 cu yds

Question 6.
FINDING THE HEIGHT OF A CYLINDER
Find the height of the cylinder at the right. Round your answer to the nearest tenth.

volume of cylinder = 43.96 cu yds

Explanation:
volume of cylinder = πr² h
where π = 3.14  diameter = 4 given
r = (4/2)
r = 2 , h = 3.5
v = 3.14 x 2 x 2 x 3.5
v = 6.28 x 2 x 3.5
v = 12.56 x 3.5
v = 43.96 cu yds

Question 7.
DIFFERENT WORDS, SAME QUESTION
Which is different? Find “both” answers.

volume of cylinder = 942 cu cm

Explanation:
volume of cylinder = πr² h
where π = 3.14  r = 5 cm
r = 5 , h = 12 given
v = 3.14 x 5 x 5 x 12
v = 3.14 x 25 x 12
v = 78.5 x 12
v = 942 cu cm

Self-Assessment for Problem Solving
Solve each exercise. Then rate your understanding of the success criteria in your journal.

Question 8.
How much salsa is missing from the jar? Explain your reasoning.

The salsa missing from the jar = 6 cm

Explanation:
Given that the jar height = 10 cm
salsa filled is 4 cm
salsa missing from the jar = 10 – 4
salsa missing from the jar = 6 cm

Question 9.
A cylindrical swimming pool has a circumference of 18π feet and a height of 4 feet. About how many liters of water are needed to fill the swimming pool to 85% of its total volume? Justify your answer. (1 ft3 ≈ 28.3 L)

The total amount of water needed to fill the swimming pool = 9 feet

Explanation:
No of liters of water = volume of cylinder = πr² h
h = 4 feet given,
circumference = 18 π feet given
2 πr = 18 π
π get canceled on both sides.
2r = 18
r = 9 feet

Question 10.
DIG DEEPER!
A company creates two designs for a cylindrical soup can. Can A has a diameter of 3.5 inches and a height of 3.6 inches. Can B has a height of 4.9 inches. Each can holds the same amount of soup. Which can requires less material to make? Explain your reasoning.

can B requires less material to make.

Explanation:
volume of the cylinder = πr² h
volume of can A = πr² h
h = 3.6 in,diameter = 3.5 in given where r = (d/2)
r = (3.5/2) = 1.75 in
v = 3.14 x 1.75 x 1.75 x 3.6
v = 3.14 x 3.0625 x 3.6
v = 3.14 x 11.025
v = 34.6185 cu in
volume of can B = πr² h
h = 4.9 in,diameter = 3.5 in given where r = (d/2)
r = (3.5/2) = 1.75 in
v = 3.14 x 3.5 x 3.5 x 3.6
v = 3.14 x 12.25 x 3.6
v = 3.14 x 44.1
v = 138.474 cu in

### Volumes of Cylinders Homework & Practice 10.1

Review & Refresh

Tell whether the triangle with the given side lengths is a right triangle.
Question 1.
20 m, 21 m, 29 m

Yes, the given side lengths form a right triangle.

Explanation:
The length of any sides of right triangle = a² + b² = c²
a² + b² = c² = a² + 2b= c²
a = 20 , b = 21, c = 29
400 + 441 = 841
841 is equal to 841

Question 2.
1 in., 2.4 in., 2.6 in.

the given side lengths is not a right triangle.

Explanation:
The length of any sides of right triangle = a² + b² = c²
a² + b² = c² = a² + 2b= c²
a = 1 , b = 2.4, c = 2.6
1+ 2.4 x 2 = 6.76
5.8 = 6.76
5.8 is not equal to 6.76

Question 3.
5.6 ft, 8 ft, 10.6 ft

the given side lengths is not a right triangle.

Explanation:
The length of any sides of right triangle = a² + b² = c²
a² + b² = c² = a² + 2b= c²
a = 5.6 , b = 8, c = 10.6
5.6 x 5.6 + 8 x 2 = 10.6 x 10.6
31.36 + 16 = 112.36
47.36 = 112.36
47.36 is not equal to 112.36

Write the number in standard form.
Question 4.
3.9 × 106

3.9000000

Explanation:
3.9 x 10⁶
3.9 x (10⁵ x 10⁶)
3.9 x (10 ⁵⁺⁶)
using aᵐx aᵑ = aᵐ⁺ᵑ
3.9 x (10 ¹¹)
3.9 x 10¹¹
3.900000000000

Question 5.
6.7 × 10-5

0.000067

Explanation:
6.7x 10-5
6.7 x 10-⁴ x 10-5
6.7 x (10-⁴- ⁵)
6.7 x 10-⁹
0.000067

Question 6.
6.24 × 1010

6.240000000000

Explanation:
6.24 x 10¹⁰
6.24 x (10⁹ x 10¹⁰)
6.24 x (10⁹ ⁺¹⁰)
using aᵐx aᵑ = aᵐ⁺ᵑ
6.24 x (10 ¹⁹ )
6.24 x 10¹⁹
6.240000000000000000000

Question 7.
Which ordered pair is the solution of the linear system 3x + 4y = -10 and 2x – 4y = 0?
A. (6, 2)
B. (2, 6)
C. (2, 1)
D. (1, 2)

option c is correct.

Explanation:
3x + 4y = -10
3 (2) + 4 (1) = -10
6 + 4 = -10
2x – 4y = 0
2 (2) – 4 (1) = 0
4 – 4 = 0

Concepts, Skills, &Problem Solving

FINDING VOLUME The height h and the base area B of a cylinder are given. Find the volume of the cylinder. Write your answer in terms of π. (See Explorations 1 and 2, p. 427.)
Question 8.
h = 5 units
B = 4π square units

volume of cylinder = 251.2 π cubic units

Explanation:
volume of cylinder = πr² h
where π = 3.14  r = 4π
r = 4π , h = 5 given
v = 3.14 x 4 x 4 x 5
v = 3.14 x 16 x 5
v = 251.2
v = 251.2 π cubic  units

Question 9.
h = 2 units
B = 25π square units

volume of cylinder = 50 π cubic units

Explanation:
volume of cylinder = πr² h
where π = 3.14  r = 25π
r = 25π , h = 2 given
v = 3.14 x 25x 25 x 2
v = 3.14 x 25 x 2
v = 3.14 x 50
v = 50 π cu. units

Question 10.
h = 4.5 units
B = 16π square units

volume of cylinder = 3,617.28 π cu. units

Explanation:
volume of cylinder = πr² h
where π = 3.14  r = 16π
r = 16π , h = 4.5 given
v = 3.14 x 16 x 16 x 4.5
v = 3.14 x 256 x 4.5
v = 3.14 x 1152
v = 3,617.28  π cu. units

FINDING THE VOLUME OF A CYLINDER Find the volume of the cylinder. Round your answer to the nearest tenth.
Question 11.

volume of cylinder = 1,526.04 cu. feet

Explanation:
volume of cylinder = πr² h
where π = 3.14  r = 9
r = 9 , h = 6 given
v = 3.14 x 9 x 9 x 6
v = 3.14 x 81 x 6
v = 3.14 x 486
v = 1,526.04 cu. feet

Question 12.

volume of cylinder = 791.28 cu. in

Explanation:
volume of cylinder = πr² h
where π = 3.14  r = 6
r = 6 , h = 7 given
v = 3.14 x 6 x 6 x 7
v = 3.14 x 36 x 7
v = 3.14 x 252
v = 791.28 cu. in

Question 13.

volume of cylinder = 769.3 cu feet

Explanation:
volume of cylinder = πr² h
where π = 3.14  r = 7
r = 7 , h = 5 given
v = 3.14 x 7 x 7 x 5
v = 3.14 x 49 x 5
v = 3.14 x 245
v = 769.3 cu feet

Question 14.

volume of cylinder = 785 cu. feet

Explanation:
volume of cylinder = πr² h
where π = 3.14  r = 5 ft
r = 5 , h = 10 given
v = 3.14 x 5 x 5 x 10
v = 3.14 x 25 x 10
v = 3.14 x 250
v = 785 cu. feet

Question 15.

volume of cylinder = 804.2 cu. cm

Explanation:
volume of cylinder = πr² h
where π = 3.14  r = 8 cm
r = 8 , h = 16 given
v = 3.14 x 8 x 8 x 16
v = 3.14 x 64 x 16
v = 3.14 x 1,024
v = 804.2 cu. cm

Question 16.

volume of cylinder = 883.125 cu. m

Explanation:
volume of cylinder = πr² h
where π = 3.14  d = 15 r = (d/2)
r = 7.5 , h = 5 given
v = 3.14 x 7.5 x 7.5 x 5
v = 3.14 x 56.25 x 5
v = 3.14 x 281.25
v = 883.125 cu. m

Question 17.
REASONING
Without calculating, which of the solids has the greater volume? Explain.

the cube has a greater volume.

Explanation:
the volume of square prism = s³
v = side x side x side
v = 8 x 8 x 8
v = 64 x 8
v = 512 cubic inches
volume of cylinder = πr² h
where π = 3.14  r = 4 cm
r = 4 , h = 8 given
v = 3.14 x 4 x 4 x 8
v = 3.14 x 16 x 8
v = 3.14 x 128
v = 401.92 cu. in

FINDING A MISSING DIMENSION Find the missing dimension of the cylinder. Round your answer to the nearest whole number.
Question 18.
Volume = 10,000 π in.3

height of cylinder = 0.080384 in

Explanation:
volume of cylinder = πr² h
where π = 3.14  d = 32 r = (d/2)
r = 16 , v = 10,000
10,000 = 3.14 x 16 x 16 x h
10,000 = 3.14 x 256 h
10,000= 803.84  h
h = (803.84/10,000)
h = 0.080384 in

Question 19.
Volume = 3785 cm3

radius of cylinder = 8 cm

Explanation:
volume of cylinder = πr² h
where π = 3.14  h = 19
v = 3785
3785 = 3.14 x r x r x 19
3785 = 3.14 x 19r²
3785= 59.66 r²
r² = (3785/59.66)
r² =64
r = 8 cm

Question 20.
Volume = 600,000 cm3

Radius of cylinder = 0.00198867 cm

Explanation:
Volume of cylinder = πr² h
where π = 3.14  h = 76 cm given
, v = 600,000
600,000 = 3.14 x r x r x 76
600,000 = 3.14 x 76r²
600,000= 238.64r²
r² = (238.64/600,000)
r² = 0.00397733
r = 0.00198867 cm

Question 21.
MODELING REAL LIFE
A cylindrical hazardous waste container has a diameter of 1.5 feet and a height of 1.6 feet. About how many gallons of hazardous waste can the container hold? (1 ft3 ≈ 7.5 gal)

Hazardous waste can hold the container = 21.195 gal

Explanation:
volume of cylinder = πr² h
where π = 3.14  d = 1.5 r = (d/2)
r = 0.75 , h = 1.6 feet
v = 3.14 x 0.75 x 0.75 x 1.6
v = 3.14 x 0.5625 x 1.6
v= 3.14 x 0.9
h = 2.826
h = 2.826 x 7.5
h = 21.195 gal

Question 22.
CRITICAL THINKING
How does the volume of a cylinder change when its diameter is halved? Explain.

the volume of the cylinder change when its diameter is halved.

Explanation:
If the diameter is halved it is the same as a radius.
d = (r/2)
(d/2)
so the volume of the cylinder change when its diameter is halved.

Question 23.
PROBLEM SOLVING
A traditional “square” bale of hay is actually in the shape of a rectangular prism. Its dimensions are 2 feet by 2 feet by4 feet. How many square bales contain the same amount of hay as one large “round” bale?

The square bales contain the same amount of hay as one large round bale = 4 squares bale

Explanation:
The surface area of rectangular prism = 2(lw + lh +wh)
given that l = 2, w=2 h = 4
area = 2(2 x 2 + 2 x 4 +4 x 2)
area = 2(4 + 8 + 8)
area = 2(2)
area = 4 sq ft

Question 24.
MODELING REAL LIFE
A tank on a road roller is filled with water to make the roller heavy. The tank is a cylinder that has a height of 6 feet and a radius of 2 feet. About how many pounds of water can the tank hold? (One cubic foot of water weighs about 62.5 pounds.)

The pounds of water can hold the tank = 4,710 pounds

Explanation:
Volume of cylinder = πr² h
where π = 3.14  h = 6 ft given
r = 2 ft
v = 3.14 x 2 x 2 x 6
v = 3.14 x 4 x 6
v= 3.14 x 24
v = 75.36 cu. feet
v = 75.36 x 62.5
v = 4,710 pounds

Question 25.
REASONING
A cylinder has a surface area of 1850 square meters and a radius of 9 meters. Estimate the volume of the cylinder to the nearest whole number.

Volume of the cylinder = 6035 cubic meters.

Explanation:
volume of the cylinder= πr²h
volume = 3.14 x 9 x 9 x 1850
volume = 8325 – 729 π
v = 8325 – 729 x 3.14
v = 8325 – 102.06
v = 8222.94
the nearest whole number to the 8222.94 is 6035 cubic meters.

Question 26.
DIG DEEPER!
Water flows at 2 feet per second through a cylindrical pipe with a diameter of 8 inches. A cylindrical tank with a diameter of 15 feet and a height of 6 feet collects the water.
a. What is the volume (in cubic inches) of water flowing out of the pipe every second?
b. What is the height (in inches) of the water in the tank after 5 minutes?
c. How many minutes will it take to fill 75% of the tank?

a. Volume of water flowing out of the pipe every second = 100.48 cu. in
b. The height of the water in tank after 5 minutes = 1,059.75 sq ft
c. 75% of water to fill tank = 25

Explanation:
a. Volume of cylinder = πr² h
where π = 3.14  h = 2 ft given
r = 4
v = 3.14 x 4 x 4 x 2
v = 3.14 x 16 x 2
v= 3.14 x 32
v = 100.48 cu. in
b. Volume of cylinder = πr² h
where π = 3.14  h = 6 ft given
r = 7.5
v = 3.14 x 7.5 x 7.5 x 6
v = 3.14 x 56.25 x 6
v= 3.14 x 337.5
v = 1,059.75 cu. ft
c. 100 – 75
25 %

Question 27.
PROJECT
You want to make and sell three different sizes of cylindrical candles. You buy 1 cubic foot of candle wax for $20 to make 8 candles of each size. a. Design the candles. What are the dimensions of each size of candle? b. You want to make a profit of$100. Decide on a price for each size of candle. Explain how you set your prices.

a. The dimensions of each size of candle = 20cm
b. price for each size of candle = $30 Explanation:$ x 80 candles given
20 x 3 = 60
each candle has a dimension of 20 cm

### Surface Areas and Volumes of Similar Solids Homework & Practice 10.4

Review & Refresh

Find the volume of the sphere. Round your answer to the nearest tenth.
Question 1.

volume of the sphere= 5,558.52222 cubic cm

Explanation:
volume of sphere = (4/3) πr² x r
v  = (4/3) x 3.14 x r³
where r =11
v = 1.33 x 3.14  x 11 x 11 x 11
v = 1.33 x 3.14 x 1,331
v = 1.33 x 4,179.34
v = 5,558.52222 cubic cm

Question 2.

volume of the sphere= 380.556225 cubic ft

Explanation:
volume of sphere = (4/3) πr² x r
v  = (4/3) x 3.14 x r³
where r =4.5
v = 1.33 x 3.14  x 4.5 x 4.5 x 4.5
v = 1.33 x 3.14 x 91.125
v = 1.33 x 286.1325
v = 380.556225 cubic ft

Question 3.

volume of the sphere=902.0592 cubic mm

Explanation:
volume of sphere = (4/3) πr² x r
v  = (4/3) x 3.14 x r³
where r =6
v = 1.33 x 3.14  x 6 x 6 x 6
v = 1.33 x 3.14 x 216
v = 1.33 x 678.24
v = 902.0592 cubic mm

Question 4.
Which system of linear equations has no solution?

Option c has no solution.

Explanation:
if we take x = 2
A. y = 4x + 1 = 4(2) + 1= 9 , y = – 4x + 1 = -8 + 1= -7
b. Y = 2x – 7 = 4 – 7 = -3 , y = 2x + 7 = 4 + 7 = 11
c. 3x + y = 1 , y = 1 – 6 y = -5 , 6x + 2y = 2 = 12 + 2y = 2,2y =- 10  y = -5
Concepts, Skills, & Problem Solving

COMPARING SIMILAR SOLIDS All of the dimensions of the solid are multiplied by a factor of k. How many times greater is the surface area of the new solid? How many times greater is the volume of the new solid? (See Exploration 1, p. 445.)
Question 5.
k = 5

25 times greater.
volume of new solid = 125 cubic ft

Explanation:
volume of  prism = lwh
where l= length, w = weight, h= height
l = 5 ,w = 5 , h = 5 given
v= 5 x 5 x 5
v = 5 x 25
v =  125  cubic ft

Question 6.
k = 10

volume of  new cone= 1,046.666 cubic cm

Explanation:
volume of  cone  =πr² (h/3)
given that r = 10 ,h = 10
v = 3.14 x 10 x 10 x (10/3)
v = 3.14 x 100 x (10/3)
v =3.14 x 100 x 3.33
v= 3.14 x 333.33
v = 1,046.666 cubic cm

IDENTIFYING SIMILAR SOLIDS Determine whether the solids are similar.
Question 7.

The solida are  similar

Explanation:
volume of  small prism = lwh
where l= length, w = weight, h= height
l = 2 ,w = 1 , h = 3 given
v= 2 x 1 x 3
v = 2 x 3
v =  6  cubic in
volume of  large prism = lwh
where l= length, w = weight, h= height
l = 6 ,w = 3 , h = 9 given
v= 6 x 3 x 9
v = 2 x 27
v =  54 cubic in

Question 8.

The solida are not similar

Explanation:
surface area  of  large prism =2 (lw + wh +1h)
where l= length, w = weight, h= height
l = 4 ,w = 2 , h = 4 given
v=2( 4 x 2 + 2 x 4 + 4 x 4)
v = 2 (8 + 8+ 16)
v =  2( 32)
v = 64 cubic in
surface area  of small prism =2 (lw + wh +1h)
where l= length, w = weight, h= height
l = 2 ,w = 1 , h = 4 given
v=2( 2 x 1 + 1 x 4 + 2 x 4)
v = 2 (2 + 4+ 8)
v =  2( 16)
v = 32 cubic in

Question 9.

The pyramids are  similar.

Explanation:
surface area of triangular pyramid 1 = area of faces + base
area of face 1 = 5
area of face 2 = 5
area of face 3 = 6.5
area of face 4 = 6
area of base = 5
A= 5 + 5 + 6.5 + 6 + 5
A = 10 + 6.5 + 11
A = 21 + 6.5
A = 27.5
surface area of triangular pyramid 2 = area of faces + base
area of face 1 = 10
area of face 2 = 10
area of face 3 = 13
area of face 4 = 12
area of base = 10
A= 10 + 10 + 13 + 12 + 10
A = 20 + 13 + 22
A = 42 + 13
A = 55

Question 10.

Two solids are not similar.

Explanation:
volume of  cone 1 =πr² (h/3)
given that  r=9 ,h = 12
v = 3.14 x 9 x 9 x (12/3)
v = 3.14 x 9 x9 x 4
v =3.14 x 81 x 4
v = 3.14 x 324
h = 1,017.36sq m
volume of  cone 2 =πr² (h/3)
given that  r=20 ,h = 21
v = 3.14 x 20 x 20 x (21/3)
v = 3.14 x20 x 20 x 7
v =3.14 x 400 x 7
v = 3.14 x 2800
h =  8,792 sq m

FINDING MISSING MEASURES IN SIMILAR SOLIDS The solids are similar. Find the missing measure(s).
Question 11.

volume of the sphere=2.5 cu. feet

Explanation:
volume of sphere = (4/3) πr² x r
v  = (4/3) x 3.14 x r³
where r =5
v = 1.33 x 3.14  x 5 x 5 x 5
v = 1.33 x 3.14 x 125
v = 1.33 x 392.5
v = 2.5 cu. feet

Question 12.

surface area of triangular pyramid  = 54 cubic m

Explanation:
surface area of triangular pyramid  = area of faces + base
area of face 1 = 12
area of face 2 = 6
area of face 3 = 13
area of face 4 = 5
area of base = 18
A= 12 + 6 + 13 + 5 + 18
A = 18 + 13 + 23
A = 18 + 36
A = 54  cubic m

Question 13.

volume = 11.5 cu. mm

Explanation:
volume of triangular prism = (bhl/2)
b = 4.6 , h = 4.6 , l = 6.4 given
v = (4.6 x 4.6 x 6.4/2)
v = (21.16 x 6.4/2)
v = (135.424/2)
v = 11.5 cu. mm

Question 14.

volume of cone = 8.0384 cu. in

Explanation:
volume of  cone  =πr² (h/3)
given that  r=1.6 ,h = 3
v = 3.14 x 1.6 x 1.6 x (3/3)
v = 3.14 x 1.6  x1.6  x 1
v =3.14 x 2.56 x 1
v = 3.14 x 2.56
v = 8.0384 cu. in

FINDING SURFACE AREA The solids are similar. Find the surface area of the red solid. Round your answer to the nearest tenth if necessary.
Question 15.

The surface area of the red solid = 90 sq m

Explanation:
Given that the surface area of blue solid = 40 sq m
s0 the surface area of the red solid = 60 sq m
4  x 10 = 40
9 x 10 = 90 sq m

Question 16.

volume of the sphere= 14,094 cu. in

Explanation:
volume of sphere = (4/3) πr² x r
v  = (4/3) x 3.14 x r³
where r =15
v = 1.33 x 3.14  x 15 x 15 x 15
v = 1.33 x 3.14 x 3375
v = 1.33 x 10,597.5
v = 14,094.675 cu. in

Question 17.
FINDING SURFACE AREA
The ratio of the corresponding linear measures of two similar cans is 4 to 7. The smaller can has a surface area of 220 square centimeters. Find the surface area of the larger can.

The surface area of larger can = 55 sq cm

Explanation:
Given that the smaller can has a surface area of 220 sq cm
The ratio of two similar cans is 4: 7
(220/5) = 55 sq cm

FINDING VOLUME The solids are similar. Find the volume of the red solid.
Question 18.

The volume of red soil =  70 cu. mm

Explanation:
surface area of triangular pyramid  = area of faces + base
area of face 1 = 21
area of face 2 = 21
area of face 3 = 7
area of face 4 = 7
area of base = 14
A= 21 + 21 + 7 + 7 + 14
A = 42 + 14 + 14
A = 42 + 28
A = 70 cu. mm

Question 19.

height  of cylinder=13,564.8 ft

Explanation:
Volume of cylinder = πr² h
where π = 3.14
r = 12
v = 3.14 x 12 x 12 x h
7850 = 3.14 x 144 h
7850= 452.16 h
h = (452.16/7850)
h = 13,564.8 sq ft

Question 20.
YOU BE THE TEACHER
The ratio of the corresponding linear measures of two similar solids is 3:5. The volume of the smaller solid is 108 cubic inches. Your friend finds the volume of the larger solid. Is your friend correct? Explain your reasoning.

Yes my friend is correct.

Explanation:
the volume of smaller solid is 108 cubic inches.
(108/v) = (3/5) x (3/5)
(108/v) = (9/25)
v = 300 cubic in

Question 21.
MODELING REAL LIFE
A hemisphere-shaped mole has a diameter of 5.7 millimeters and a surface area of about 51 square millimeters. The radius of the mole doubles. Estimate the new surface area of the mole.

The new surface area of the mole = 19.742 sq. mm

Explanation:
surface area of sphere = (4/3) πr² x r
A = (4/3) x 3.14 x r³
where r = 2.85
A = 1.33 x 3.14  x 2.85 x 2.85
A= 1.33 x 3.14 x 8.1225
A = 1.33 x 25.50465
A = 19.742 sq. mm

Question 22.
REASONING
The volume of a 1968 Ford Mustang GT engine is 390 cubic inches. Which scale model of the Mustang has the greater engine volume, a 1 : 18 scale model or a 1 : 24 scale model? How much greater is it?

Question 23.
DIG DEEPER!
You have a small marble statue of Wolfgang Mozart. It is 10 inches tall and weighs 16 pounds. The original marble statue is 7 feet tall.

a. Estimate the weight of the original statue. Explain your reasoning.
b. If the original statue were 20 feet tall, how much would it weigh?

a. The weight of the original statue = 84/10 cubic pounds
b. The original statue weight = 221 lb

Explanation:
a. The weight of the original statue = 7 ft
1 ft = 12 pounds
7 x 12 / 10 = 84/10 cubic pounds.
b. given that the original statue was 20 ft
221,184 lb

Question 24.
REPEATED REASONING
The nesting dolls are similar. The largest doll is 7 inches tall. Each of the other dolls is 1 inch shorter than the next larger doll. Make a table that compares the surface areas and the volumes of the seven dolls.

Explanation:
In the above given figure the larger doll is 7 inches tall.
Each of the other doll is 1 inch shorter than the next larger doll.

Question 25.
PRECISION
You and a friend make paper cones to collect beach glass. You cut out the largest possible three-fourths circle from each piece of paper.

a. Are the cones similar? Explain your reasoning.
b. Your friend says that because your sheet of paper is twice as large, your cone will hold exactly twice the volume of beach glass. Is this true? Explain your reasoning.

a. Yes, the cones are similar.
b.No my friend is correct.

Explanation:
a. all circles are similar, the slant height and the circumference of the base of the cones are proportional .
b. my cone holds about 2 times as much my friend cone.

### Volume and Similar Solids Connecting Concepts

Using the Problem-Solving Plan
Question 1.
A yurt is a dwelling traditionally used in Mongolia and surrounding regions. The yurt shown is made of a cylinder and a cone. What is the volume of the yurt?

Understand the problem
You know that the yurt is made of a cylinder and a cone. You also know several dimensions. You are asked to find the volume of the yurt.
Make a plan.
Use the Pythagorean Theorem to find the height of the cone. Then use the formulas for the volume of a cylinder and the volume of a cone to find the volume of the yurt.
Solve and check.
Use the plan to solve the problem. Then check your solution.

volume of hurt = 4855 cu. ft

Explanation:
volume of  cone  =πr² (h/3)
given that  r = 15 ,h = 7
v = 3.14 x 15 x 15 x (17/3)
v = 3.14 x 225  x (17/3)
v =3.14 x 225 x 5.666
v = 3.14 x 1275
v = 4,003
volume of cylinder = πr² h
where π = 3.14  d =
r = 3 , h = 30
v = 3.14 x 3 x 3 x 30
v = 3.14 x 9 x 30
v= 3.14 x 270
h = 847.8
4008 +847 =4855

Question 2.
supervoidA spherical , a region in space that is unusually empty, has a diameter of 1.8 × 19 0light-years. What is the volume of the supervoid? Use 3.14 for π. Write your answer in scientific notation.

volume of supervoid =3.75858000000000 light years

Explanation:
volume of sphere = (4/3) πr³
v = (4/3) x 3.14 x r³
v = 1.33 x 3.14 x 0.9
v = 2.826 x 1.33
v = 3.75858000000000 light years

Question 3.
The cylinders are similar. The volume of Cylinder A is $$\frac{8}{27}$$ times the volume of Cylinder B. Find the volume of each cylinder. Round your answers to the nearest tenth.

volume of cylinder = 452.16 cu. cm

Explanation:
the volume of cylinder = πr² h
where π = 3.14
r = 4 , h = 9
v = 3.14 x 4 x 4 x 9
v = 3.14 x 16 x 9
v= 3.14 x 144
h = 452.16 sq cm

Packaging Salsa
At the beginning of this chapter, you watched a STEAM Video called “Canning Salsa.” You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.

### Volume and Similar Solids Chapter Review

Review Vocabulary

Write the definition and give an example of each vocabulary term.

Graphic Organizers

You can use a Summary Triangle to explain a concept. Here is an example of a Summary Triangle for volume of a cylinder.

Choose and complete a graphic organizer to help you study the concept.

1. volume of a cone
2. volume of a sphere
3. volume of a composite solid
4. surface areas of similar solids
5. volumes of similar solids

cone = A solid or hollow object which tapers from a circular or roughly circular base to a point.
hemisphere = a half of the celestial sphere as divided into two halves by the horizon.
sphere = a round solid figure, or its surface, with every point on its surface equidistant from its center.
similar solids = two solids are similar if they are the same type of solid and their corresponding radii, heights, base lengths, widths, etc. are proportional.

Chapter Self-Assessment

As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.

10.1 Volumes of Cylinders (pp. 427–432)
Learning Target: Find the volume of a cylinder. Find the volume of the cylinder. Round your answer to the nearest tenth.
Question 1.

volume of cylinder =1,236.375 cu. ft

Explanation:
volume of cylinder = πr² h
where π = 3.14  d = 15 r = (d/2)
r = 7.5 , h = 7 given
v = 3.14 x 7.5 x 7.5 x 7
v = 3.14 x 56.25 x 7
v = 3.14 x 393.75
v = 1,236.375 cu. ft

Question 2.

volume of cylinder =62.8 cu. cm

Explanation:
volume of cylinder = πr² h
where π = 3.14
r = 2 , h = 5 given
v = 3.14 x 2 x 2 x 5
v = 3.14 x 4 x 5
v = 3.14 x 20
v = 62.8 cu. cm

Find the missing dimension of the cylinder. Round your answer to the nearest whole number.
Question 3.

height of cylinder = 0.25232143 sq in

Explanation:
volume of cylinder = πr² h
where π = 3.14
r = 1.5 , v = 28 given
28 = 3.14 x 1.5 x 1.5 x h
28= 3.14 x 2.25h
28 = 7.065 h
h = 7.065/28
h = 0.25232143 sq in

Question 4.

radius of cylinder =60.501 sq m

Explanation:
volume of cylinder = πr² h
where π = 3.14
h = 20 m, v = 7599 given
7599= 3.14 x r x r x 20
7599= 3.14 x 20 r²
7599 = 62.8 r²
r² = 7599/62.8
r² = 121.00 m
r = 60.501 sq m

Question 5.
You are buying two cylindrical cans of juice. Each can holds the same amount of juice.

a. What is the height of Can B?
b. About how many cups of juice does 3≈each can hold? (1 in.3 ≈ 0.07 cup)

a.The height of can B = 0.074 in
b. The cups of juice does 3 each can hold = 21 cups

Explanation:
volume of cylinder = πr² h
where π = 3.14
h = 6, r = 3given
v = 3.14 x 3 x 3 x 6
v= 3.14 x 9 x 6
v = 3.14 x 54
v = 169.56 sq in
volume of cylinder = πr² h
where π = 3.14
v = 169.56, r = 2given
169.56 = 3.14 x 2 x 2 h
169.56= 3.14 x 4 h
169.56= 12.56 h
h = 0.074 in
b. 3 x 0.07
0.21
21 cups.

Question 6.
You triple the radius of a cylinder. How many times greater is the volume of the new cylinder? Explain.

3 times greater than the volume of the new cylinder.

Explanation:
Given that the radius is tripled.
volume of cylinder = πr⁵ h

10.2 Volumes of Cones (pp. 433–438)
Learning Target: Find the volume of a cone.

Find the volume of the cone. Round your answer to the nearest tenth.
Question 7.

volume of  cone= 803.84 cu. m

Explanation:
volume of  cone  =πr² (h/3)
given that r = 8 ,h = 12
v = 3.14 x 8 x 8 x (12/3)
v = 3.14 x 64 x (12/3)
v =3.14 x 64 x 4
v= 3.14 x 256
v = 803.84 cu. m

Question 8.

volume of  cone= 41.8666 cu. cm

Explanation:
volume of  cone  =πr² (h/3)
given that r = 2 ,h = 10
v = 3.14 x 2 x 2 x (10/3)
v = 3.14 x 4 x (10/3)
v =3.14 x 4 x 3.33
v= 3.14 x 13.33
v = 41.8666 cu. cm

Find the missing dimension of the cone. Round your answer to the nearest tenth.
Question 9.

Explanation:
volume of  cone  =πr² (h/3)
given that ,h = 36
3052= 3.14 x r x r (36/3)
3052 = 3.14 x 12 r²
3052 =37.68 r²
r²= 0.012346
v = 0.006173 cu. in

Question 10.

height of  cone=0.041866 sq mm

Explanation:
volume of  cone  =πr² (h/3)
given that ,r =6
900= 3.14 x 6 x 6 (h/3)
900 = 3.14 x 12 h
900 =37.68 h
h= (37.68/900)
h  = 0.041866 sq mm

Question 11.
The paper cup can hold 84.78 cubic centimeters of water. What is the height of the cup?

height of  cone=  0.111111 cm

Explanation:
volume of  cone  =πr² (h/3)
given that ,r =3
84.78= 3.14 x 3 x 3 (h/3)
84.78 = 3.14 x 3 h
84.78 =9.42 h
h= (9.42/84.78)
h  = 0.111111 cm

10.3 Volumes of Spheres (pp. 439–444)
Learning Target: Find the volume of a sphere.

Find the volume of the sphere. Round your answer to the nearest tenth.
Question 12.

volume of the sphere=7,216.4736 cubic ft

Explanation:
volume of sphere = (4/3) πr² x r
v  = (4/3) x 3.14 x r³
where r =12
v = 1.33 x 12  x 12 x 12 x 3.14
v = 1.33 x 3.14 x 1728
v = 1.33 x 5,425.92
v = 7,216.4736 cubic ft

Question 13.

volume of the sphere= 5,558.52222 cu. cm

Explanation:
volume of sphere = (4/3) πr² x r
v  = (4/3) x 3.14 x r³
where r =11
v = 1.33 x 11  x 11 x 11 x 3.14
v = 1.33 x 3.14 x 1331
v = 1.33 x 4,179.34
v = 5,558.52222 cu. cm

Question 14.
The volume of a water walking ball is $$\frac{4}{3}$$π cubic meters. Find the diameter of the water walking ball.

Find the volume of the composite solid. Round your answer to the nearest tenth if necessary.
Question 15.

volume of  cone=  452.16 cu. m

Explanation:
volume of  cone  =πr² (h/3)
given that ,r = 6, h = 12
v= 3.14 x 6 x 6 (12/3)
v = 3.14 x 36 x (12/3)
v =3.14 x 36 x 4
v= 3.14 x 144
v  = 452.16 cu. m

Question 16.

The volume of solid=  31 cu. ft

Explanation:
surface area of triangular pyramid  = area of faces + base
area of face 1 = 6
area of face 2 = 6
area of face 3 = 2
area of face 4 = 5
area of base = 12
A= 6 + 6 + 2 + 5 + 12
A = 12 + 7 + 12
A = 24 + 7
A = 31   sq ft

Question 17.

volume of cylinder =50.24 cu. cm

Explanation:
volume of cylinder = πr² h
where π = 3.14
r = 2 , h = 4 given
v = 3.14 x 2 x 2 x 4
v = 3.14 x 16
v= 50.24 cu. cm

Question 18.
The volume of water that a submerged object displaces is equal to the volume of the object. Find the radius of the sphere. Round your answer to the nearest tenth.(1 mL = 1 cm3)

10.4 Surface Areas and Volumes of Similar Solids (pp. 445–452)
Learning Target: Find the surface areas and volumes of similar solids.

Question 19.
Determine whether the solids are similar.

Volume of cylinder= 0.17840909 cu. cm

Explanation:
Volume of cylinder = πr² h
where π = 3.14
r = 2.5
110 = 3.14 x 2.5 x 2.5 x h
110 = 3.14 x 6.25 h
110= 19.625 h
h = (19.625/110)
h = 0.17840909 sq cm

Question 20
The prisms are similar. Find the missing measures.

Question 21.
The prisms are similar. Find the surface area of the red prism. Round your answer to the nearest tenth.

volume = 67.712 cubic cm

Explanation:
volume of triangular prism = (bhl/2)
b = 4.6 , h = 4.6 , l = 6.4 given
v = (4.6 x 4.6 x 6.4/2)
v = (21.16 x 6.4/2)
v = (135.424/2)
v = 67.712 cubic  cm

Question 22.
The pyramids are similar. Find the volume of the red pyramid.

The volume of red soil =  70 cu. mm

Explanation:
surface area of triangular pyramid  = area of faces + base
area of face 1 = 21
area of face 2 = 21
area of face 3 = 7
area of face 4 = 7
area of base = 14
A= 21 + 21 + 7 + 7 + 14
A = 42 + 14 + 14
A = 42 + 28
A = 70  sqmm

Question 23.
The ratio of the corresponding linear measures of two similar jewelry boxes is 2 to 3. The larger jewelry box has a volume of 162 cubic inches. Find the volume of the smaller jewelry box.

volume of the jewelry box = 36.4 cubics in

Explanation:
given that 2: 3 ratio
(162/v) = (2/3) x (2/3)
(162/v) = (4/9)
4v = 1458
v = (1458/4)
v = 36.4 cubic in

### Volume and Similar Solids Practice Test

Find the volume of the solid. Round your answer to the nearest tenth.
Question 1.

volume of the sphere=33,409.6 cu. mm

Explanation:
volume of sphere = (4/3) πr² x r
v  = (4/3) x 3.14 x r³
where r =20
v = 1.33 x 20 x 20 x 20 x 3.14
v = 1.33 x 3.14 x 8000
v = 1.33 x 25,120
v = 33,409.6 cu. mm

Question 2.

volume of  cone=  452.16 cu. m

Explanation:
volume of  cone  =πr² (h/3)
given that ,r = 6, h = 12
v= 3.14 x 6 x 6 (12/3)
v = 3.14 x 36 x (12/3)
v =3.14 x 36 x 4
v= 3.14 x 144
v  = 452.16 cu. m

Question 3.

volume of the sphere=33,409.6 cu. mm

Explanation:
volume of sphere = (4/3) πr² x r
v  = (4/3) x 3.14 x r³
where r =20
v = 1.33 x 20 x 20 x 20 x 3.14
v = 1.33 x 3.14 x 8000
v = 1.33 x 25,120
v = 33,409.6 cu. mm

Question 4.

volume of  cone=  452.16 cu. m

Explanation:
volume of  cone  =πr² (h/3)
given that ,r = 6, h = 12
v= 3.14 x 6 x 6 (12/3)
v = 3.14 x 36 x (12/3)
v =3.14 x 36 x 4
v= 3.14 x 144
v  = 452.16 cu. m

Question 5.
The pyramids are similar.

a. Find the missing measures.
b. Find the surface area of the red pyramid.

The volume of red soil =  70 cu. mm

Explanation:
surface area of triangular pyramid  = area of faces + base
area of face 1 = 21
area of face 2 = 21
area of face 3 = 7
area of face 4 = 7
area of base = 14
A= 21 + 21 + 7 + 7 + 14
A = 42 + 14 + 14
A = 42 + 28

Question 6.
You are making smoothies. You will use either the cone-shaped glass or the cylindrical glass. Which glass holds more? About how much more?

volume of  cone=  452.16 cu. m

Explanation:
volume of  cone  =πr² (h/3)
given that ,r = 6, h = 12
v= 3.14 x 6 x 6 (12/3)
v = 3.14 x 36 x (12/3)
v =3.14 x 36 x 4
v= 3.14 x 144
v  = 452.16 cu. m

Question 7.
The ratio of the corresponding linear measures of two similar waffle cones is 3 to 4. The smaller cone has a volume of about 18 cubic inches. Find the volume of the larger cone. Round your answer to the nearest tenth.

Explanation:
(18/v) = (3/4)
3v = 18 x 4
3v = 72
v = 24 cubic in

Question 8.
Draw two different composite solids that have the same volume but different surface areas.Explain your reasoning.

Question 9.
There are 13.5π cubic inches of blue sand and 9π cubic inches of red sand in the cylindrical container. How many cubic inches of white sand are in the container? Round your answer to the nearest tenth.

v = 169.56 cu. in
Explanation:
volume of cylinder = πr² h
where π = 3.14
h = 6, r = 3given
v = 3.14 x 3 x 3 x 6
v= 3.14 x 9 x 6
v = 3.14 x 54
v = 169.56 cu. in

Question 10.
Without calculating, determine which solid has the greater volume. Explain your reasoning.

prism has great volume.

Explanation:
the volume of the sphere is less than the volume of a prism.

### Volume and Similar Solids Cumulative Practice

Question 1.
What is the value of 14 – 2$$\sqrt [ 3 ]{ 64 }$$ ?
A. – 50
B. – 2
C. 6
D. 48
option A Is correct

Explanation:
14 – 2 (3/64 x 100)
12 (150/32)
12 x (75/16)
-50

Question 2.
What is the volume of the cone? (Use $$\frac{22}{7}$$ for π.)

volume of  cone=  4098. 8304 cubic cm

Explanation:
volume of  cone  =πr² (h/3)
given that ,r = 14, h = 20
v= 3.14 x 14 x 14 (20/3)
v = 3.14 x196 x (20/3)
v =3.14 x 196 x 6.66
v= 3.14 x 1305.36
v  = 4098. 8304

Question 3.
The cylinders are similar. What is the volume of the red cylinder?

A. 6 cm
B. 150.75 cm3
C. 301.5 cm3
D. 603 cm3

option D is correct.

Explanation:
(1206/2 ) = 603
large cylinder is 2 times greater than small cylinder.

Question 4.
A rectangle is graphed in the coordinate plane.

Which of the following shows Rectangle E’F’G’H’, the image of Rectangle EFGH after it is reflected in the -axis?

option  I is correct.

Explanation:
EFGH  is reflected in the -ve axis.

Question 5.
What are the ordered pairs shown in the mapping diagram?

A. (2, 5), (4, – 2), (6, – 7), (8, 1)
B. (2, – 7), (4, – 2), (6, 1), (8, 5)
C. (2, 5), (4, 1), (6, – 2), (8, – 7)
D. (5, 2), (- 2, 4), (- 7, 6), (1, 8)

option A is correct.

Explanation:
(2, 5)
(4, -2)
(6, -7)
(8, 1)

Question 6.
What is $$0 . \overline{75}$$ written as a fraction?

Question 7.
Solve the formula A = P + PI for I.

option I is correct.

Explanation:
A = P + PI
I = (A – P/P)
A = P + P (A – P/P)
A = A.

Question 8.
A cylinder has a volume of 1296 cubic inches. If you divide the radius of the cylinder by 12, what is the volume (in cubic inches) of the smaller cylinder?

The volume =0.1162963 cubic in

Explanation:
volume of  cylinder  =πr² (h/3)
given that r = 12 , v = 1296
1296 = 3.14 x 12 x 12 x (h/3)
1296 = 3.14 x 12x 4h
1296 =3.14 x  48 h
1296= 150.72 h
h =(150.72/1296)
h = 0.1162963 cubic in

Question 9.
The cost y (in dollars) for pounds of grapes is represented by y = 2x. Which graph represents the equation?

Option c is correct.

Explanation:
y = 2x
on the x axis the graph represents the straight line on x – axis.

Question 10.
You are making a giant crayon. What is the volume (in cubic centimeters) of the entire crayon? Show your work and explain your reasoning. (Use 3.14 for π.)

The volume = =75.34116 cubic cm

Explanation:
the volume of  cylinder  =πr² (h/3)
given that r = 3 ,h = 8
v = 3.14 x 3 x 3 x (8/3)
v = 3.14 x 9 x (8/3)
v =3.14 x 9 x 2.666
v= 3.14 x 23.994
v = 75.34116 cubic cm

Conclusion:

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