Go through the Spectrum Math Grade 6 Answer Key Chapter 6 Lesson 6.4 Volume of Rectangular Solids and get the proper assistance needed during your homework.
Spectrum Math Grade 6 Chapter 6 Lesson 6.4 Volume of Rectangular Solids Answers Key
The volume (V) of a rectangular solid is the product of the measure of its length (l), the measure of its width (w), and the measure of its height (h). V = l × w × h
V= 10 × 5 × 6
= 50 × 6
= 300
The volume is 300 cubic feet.
Find the volume of each rectangular solid.
Question 1.
a.
V = ___ cu. yd.
Answer:
Given cuboid is 12 yd. long, 5 yd. wide and 7 yd. high
Volume of cuboid = length×width×height
= 12×5×7
= 420 cu.yd.
b.
V = ___ cu. in.
Answer:
Given cube is 8 in. long.
Volume of cube = length×length×length
= 8×8×8
= 512 cu.in
c.
V = ___ cu. ft.
Answer:
Given cuboid is 20 ft. long, 15 ft. wide and 40 ft. high
Volume of cuboid = length×width×height
= 15×20×40
= 420 cu.ft.
Question 2.
a.
V = ___ cu. ft.
Answer:
Given cuboid is 6 ft. long, 4 ft. wide and 14 ft. high
Volume of cuboid = length×width×height
= 6×4×14
= 336 cu.ft.
b.
V = ___ cu. in.
Answer:
Given cuboid is 5 in. long, 4 in. wide and 5 in. high
Volume of cuboid = length×width×height
= 5×5×4
= 100 cu.in.
c.
V = ___ cu. in.
Answer:
Given cuboid is 12 in. long, 6 in. wide and 9 in. high
Volume of cuboid = length×width×height
= 12×6×9
= 648 cu.in.
Find the volume of each rectangular solid.
Question 1.
a.
V = ____ cu. cm
Answer:
Given cuboid is 12 cm long, 6 cm wide and 8 cm high
Volume of cuboid = length×width×height
= 12×6×8
= 576 cu.cm.
b.
V = ____ cu. mm
Answer:
Given cube is 12 mm long.
Volume of cube = length×length×length
= 12×12×12
= 1728 cu.mm
c.
V = ____ cu. m
Answer:
Given cuboid is 22 m long, 8 m wide and 12 m high
Volume of cuboid = length×width×height
= 22×8×12
= 2112 cu.m.
Question 2.
a.
V = ____ cu. mm
Answer:
Given cuboid is 8 mm long, 3 mm wide and 6 mm high
Volume of cuboid = length×width×height
= 8×3×6
= 144 cu.mm.
b.
V = ____ cu. mm
Answer:
Given cuboid is 15 mm long, 12 mm wide and 9 mm high
Volume of cuboid = length×width×height
= 15×12×9
= 1620 cu.mm.
c.
V = ____ cu. cm
Answer:
Given cuboid is 15 cm long, 12 cm wide and 20 cm high
Volume of cuboid = length×width×height
= 15×12×20
= 3600 cu.cm.
Question 3.
a.
V = ____ cu. mm
Answer:
Given cuboid is 20 mm long, 8 mm wide and 8 mm high
Volume of cuboid = length×width×height
= 8×20×8
= 1280 cu.mm.
b.
V = ____ cu. cm
Answer:
Given cuboid is 30 cm long, 20 cm wide and 20 cm high
Volume of cuboid = length×width×height
= 30×20×20
= 12000 cu.cm.
c.
V = ____ cu. mm
Answer:
Given cuboid is 26 mm long, 20 mm wide and 15 mm high
Volume of cuboid = length×width×height
= 26×20×15
= 7800 cu.mm.
The volume of a rectangular solid with fractional edge lengths can also be measured by packing the solid with cubes that share a common denominator with the edge lengths. In this rectangular solid, each side length has a denominator of 5, so the solid can be packed with inch cubes to determine its volume.
First, calculate the volume of the cube itself.
\(\frac{1}{5}\) × \(\frac{1}{5}\) × \(\frac{1}{5}\) = \(\frac{1}{125}\) cubic inches
Next, add up the cubes in the solid. You can see from the top layer that there are 12 cubes per layer, and 12 × 3 = 36.
Last multiply the number of cubes times the volume of one cube.
36 × \(\frac{1}{125}\) = \(\frac{36}{125}\) cubic inches
This is the same answer you get when you use the formula l × w × h.
\(\frac{4}{5}\) × \(\frac{3}{5}\) × \(\frac{3}{5}\) = \(\frac{36}{125}\)
Find the volume of each rectangular solid.
Question 1.
a.
V = ____ cu. in.
Answer:
Given cube is \(\frac{2}{7}\) in. long.
Volume of cube = length×length×length
= \(\frac{2}{7}\)×\(\frac{2}{7}\)×\(\frac{2}{7}\)
= \(\frac{8}{343}\)
Thus, the volume will be \(\frac{8}{343}\) cu.in
b.
V = ____ cu. ft.
Answer:
Given cuboid is \(\frac{6}{9}\) ft long, \(\frac{2}{9}\) ft wide and \(\frac{1}{9}\) ft high
Volume of cuboid = length×width×height
= \(\frac{6}{9}\)×\(\frac{2}{9}\)×\(\frac{1}{9}\)
= \(\frac{12}{729}\)
Thus, the volume will be \(\frac{12}{729}\) cu.ft
Question 2.
a.
V = ____ cu. cm
Answer:
Given cuboid is \(\frac{4}{9}\) cm long, \(\frac{8}{9}\) cm wide and \(\frac{5}{9}\) cm high
Volume of cuboid = length×width×height
= \(\frac{4}{9}\)×\(\frac{8}{9}\)×\(\frac{5}{9}\)
= \(\frac{160}{729}\)
Thus, the volume will be \(\frac{}{729}\) cu.cm
b.
V = ____ cu. ft.
Answer:
Given cuboid is \(\frac{10}{11}\) ft long, \(\frac{2}{11}\) ft wide and \(\frac{2}{11}\) ft high
Volume of cuboid = length×width×height
= \(\frac{10}{11}\)×\(\frac{2}{11}\)×\(\frac{2}{11}\)
= \(\frac{40}{1331}\)
Thus, the volume will be \(\frac{40}{1331}\) cu.ft