Go through the Spectrum Math Grade 6 Answer Key Chapter 6 Posttest and get the proper assistance needed during your homework.
Spectrum Math Grade 6 Chapter 6 Posttest Answers Key
Check What You Learned
Geometry
Find the area or surface area of each figure.
Question 1.
a.
A = ___ sq. in.
Answer:
Given rectangle is 14m long and 28m wide.
Area of rectangle = length×width
= 14×28
= 392 sq.m
b.
A = ___ sq. cm
Answer:
Given triangle has base length of 42 in. and height of 15 in.
A = \(\frac{1}{2}\) × b × h
= \(\frac{1}{2}\) × 42 × 15
= \(\frac{1}{2}\) × 630
= 315
Thus, the area will be 315 square inches
c.
A = ___ sq. cm
Answer:
The base of the triangle will be 8-4=4 in and the height will be 10-6=4 in.
Area of triangle = \(\frac{1}{2}\) × b × h
= \(\frac{1}{2}\) × 4 × 4
= \(\frac{1}{2}\) × 16
= 8 sq.in.
Area of rectangle with length 10 in long and 8 in. wide will be length×width
= 10×8
= 80 sq.in.
Area of the figure will be the difference of the area of triangle from area of rectangle
Area of figure = Area of rectangle – Area of triangle
= 80-8
= 72 sq.in.
Question 2.
a.
A = ___ sq. in.
Answer:
Given figure has base length of 11.5 in. and height of 5.7 ft.
Area of parallelogram = base × height
= 11.5 × 5.7
= 65.55
Thus, the area of parallelogram will be 65.55 sq.in.
b.
SA = ___ sq. m.
Answer:
Given rectangular solid is 6.5 m wide, 9 m long and 7 m high
Surface area of the solid = 2×(length×width + width×height + height×length)
= 2×(9×6.5 + 6.5×7 + 7×9)
= 2×(58.5+45.5+63)
=2×167
=334 sq.m
The surface area of the rectangular solid is 1376 sq.m
c.
SA = ___ sq. m.
Answer:
Given that side length is 14 m and the slant height is 16 m
The surface area for the given pyramid = s2 + 2sl
Where s =14 m and l =16 m
= 14×14 + 2×14×16
= 196 + 448
= 644
Thus, the surface area of the given pyramid will be 644 sq.m
Find the volume of each rectangular solid.
Question 3.
a.
V = ___ cu. m
Answer:
Given cuboid is 20 m long, 14 m wide and 12 m high
Volume of cuboid = length×width×height
= 20×14×12
= 3360 cu.m
Thus, the volume will be 3360 cu.m
b.
V = ___ cu. mm
Answer:
Given cuboid is 16 mm long, 3 mm wide and 4 mm high
Volume of cuboid = length×width×height
= 16×3×4
= 192 cu.mm
Thus, the volume will be 192 cu.mm
c.
V = ___ cu. cm
Answer:
Given cuboid is 15 cm long, 8 cm wide and 10 cm high
Volume of cuboid = length×width×height
= 15×8×10
= 1200 cu.mm
Thus, the volume will be 1200 cu.mm
Use the coordinate grids to find the missing vertex of each polygon.
Question 4.
a. a rectangle with points at (5, 2), (-2, 2), and (5, -4)
The missing point is at _________
Answer:
Let us assume the given points (5, 2), (-2, 2), and (5, -4) as A,B and C respectively.
Connect the vertices A,B,C and then draw lines straight from points A and C.
The intersecting point of both will be the point D.
Thus, point D will be (-2,-4)
b. a right triangle with points at (-1, 3) and (2, 3)
The missing point is at _________ or _______
Answer:
Let us assume the given points (-1, 3) and (2, 3) as A and B respectively.
If points A (-1, 3) and B (2, 3) are vertices of the hypotenuse of a right triangle.
Connect the vertices and then draw lines straight from points A and B.
The intersecting points will be the missing point.
Point C can be (4,2) or (-5,-3)
Solve each problem.
Question 5.
A piece of metal is shaped like a right triangle. Its base is 18 feet and its height is 24 feet. What is its area?
The area is ________ square feet.
Answer:
Given that a piece of metal is shaped like a right triangle with base length of 18 ft and height of 24 ft.
Area of triangle = \(\frac{1}{2}\) × b × h
= \(\frac{1}{2}\) × 18 × 24
= \(\frac{1}{2}\) × 432
= 216
The area is 216 square feet.
Question 6.
Stephanie’s hamster cage is 20 inches long, 12 inches wide, and 10 inches deep. What is the volume of the cage?
The volume is __________ cubic inches.
Answer:
Given that Stephanie’s hamster cage is 20 inches long, 12 inches wide, and 10 inches deep.
Volume of cuboid = length×width×height
= 20×12×10
= 2400
The volume is 2400 cubic inches.
Question 7.
Pablo’s snake cage is 30 inches long, 15 inches wide, and 12 inches deep. What is the volume of the cage?
The volume of the cage is _________ cubic inches.
What is the volume of the cage in cubic feet?
The volume of the cage is _________ cubic feet.
Answer:
Given that the Pablo’s snake cage is 30 inches long, 15 inches wide, and 12 inches deep.
Volume of cuboid = length×width×height
= 30×15×12
= 5400
The volume of the cage is 5400 cubic inches.
1 ft equals to 12 in.
To convert the inches to feet, divide the inches by 12
= 5400÷12
= 450
The volume of the cage is 450 cubic feet.