Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 22.2 Volume of Solid Figures to secure good marks & knowledge in the exams.
McGraw-Hill Math Grade 8 Answer Key Lesson 22.2 Volume of Solid Figures
Exercises
CALCULATE VOLUME
Question 1.
Answer:
Volume of the cylinder = 282.857 cubic feet.
Explanation:
Height of the cylinder = 10 ft.
Radius of the cylinder = 3 ft.
Volume of the cylinder =  π r² h
= π × 3 × 3 × 10
= π × 9 × 10
= π × 90
= \(\frac{22}{7}\) × 90 (As π = \(\frac{22}{7}\))
= \(\frac{1980}{7}\)
= 282.857 cubic feet.
Question 2.
Answer:
Volume of the cuboid = 36 cubic feet.
Explanation:
Length of the cuboid = 6 ft.
Width of the cuboid = 3 ft.
Height of the cuboid = 2ft.
Volume of the cuboid = Length of the cuboid × Width of the cuboid × Height of the cuboid)
= 6 × 3 × 2
= 18 × 2
= 36 cubic feet.
Question 3.
Answer:
Volume of the cube = 64 cubic cm.
Explanation:
Side of the cube = 4 cm.
Volume of the cube = Side of the cube × Side of the cube × Side of the cube
= 4 × 4 × 4
= 16 × 4
= 64 cubic cm.
Question 4.
Answer:
Volume of the cylinder = 1357.714 cubic in.
Explanation:
Height of the cylinder = 12 in.
Radius of the cylinder = 6 in.
Volume of the cylinder = π r2 h
= π × 6 × 6 × 12
= π × 36 × 12
= π × 432
= \(\frac{22}{7}\) × 432 (As π = \(\frac{22}{7}\))
= \(\frac{9504}{7}\)
= 1357.714 cubic in.
Question 5.
Answer:
Volume of the cuboid = 140 cubic cm.
Explanation:
Length of the cuboid = 7 cm.
Width of the cuboid = 5 cm
Height of the cuboid = 4 cm.
Volume of the cuboid = Length of the cuboid × Width of the cuboid × Height of the cuboid
= 7 × 5 × 4
= 35 × 4
= 140 cubic cm.
Question 6.
Answer:
Volume of the cylinder = 50.285 cubic ft.
Explanation:
Height of the cylinder = 4 ft.
Radius of the cylinder = 2 ft.
Volume of the cylinder = πr²h
= π × 2 × 2 × 4
= π × 4 × 4
= π × 16
= \(\frac{22}{7}\) × 16  (As π = \(\frac{22}{7}\))
= \(\frac{352 }{7}\)
= 50.285 cubic ft.
Question 7.
Answer:
Volume of the pyramid = 480 cubic ft.
Explanation:
Length of the pyramid = 12 ft.
Width of the pyramid = 12 ft.
Height of the pyramid = 10 ft.
Volume of the pyramid = \(\frac{1}{3}\) × Length of the pyramid × Width of the pyramid × Height of the pyramid
= \(\frac{1}{3}\) × 12 × 12 × 10
= \(\frac{1}{1}\) × 4 × 12 × 10
= 48 × 10
= 480 cubic ft.
Question 8.
Answer:
Volume of cone = 100.571 cubic ft.
Explanation:
Radius of the cone = 4 ft.
Height of the cone = 6 ft.
Volume of cone = 1/3hπr²
= \(\frac{1}{3}\) × 6 × π × 4 × 4
= \(\frac{1}{1}\) × 2 × π × 16
= π × 32
= \(\frac{22}{7}\) × 32  (As π = \(\frac{22}{7}\))
= \(\frac{704}{7}\)
= 100.571 cubic ft.
Question 9.
Answer:
Volume of the pyramid = 32 cubic yd.
Explanation:
Length of the pyramid = 4 yd.
Width of the pyramid = 4 yd.
Height of the pyramid = 6 yd.
Volume of the pyramid = \(\frac{1}{3}\) × Length of the pyramid × Width of the pyramid × Height of the pyramid
= \(\frac{1}{3}\) × 4 × 4 × 6
= \(\frac{1}{1}\) × 4 × 4 × 2
= 16 × 2
= 32 cubic yd.
Question 10.
Answer:
Volume of cone = 1,508.571 cubic ft.
Explanation:
Radius of the cone = 12 ft.
Height of the cone = 10 ft.
Volume of cone = 1/3hπr²
= \(\frac{1}{3}\) × 10 × π × 12 × 12
= \(\frac{1}{3}\) × 10 × π × 144
= \(\frac{1}{3}\) × 1440 × π
= \(\frac{1440}{3}\) × π
= \(\frac{1440}{3}\) × \(\frac{22}{7}\)   (As π = \(\frac{22}{7}\))
= \(\frac{31680}{21}\)
=Â 1,508.571 cubic ft.
Question 11.
Answer:
Volume of the pyramid = 140 cubic ft.
Explanation:
Length of the pyramid = 7 ft.
Width of the pyramid = 5 ft.
Height of the pyramid = 12 ft.
Volume of the pyramid = \(\frac{1}{3}\) × Length of the pyramid × Width of the pyramid × Height of the pyramid
= \(\frac{1}{3}\) × 7 × 5 × 12
= \(\frac{1}{1}\) × 7 × 5 × 4
= 35 × 4
= 140 cubic ft.
Question 12.
Answer:
Volume of cone = 103.714 cubic ft.
Explanation:
Radius of the cone = 3 ft.
Height of the cone = 11 ft.
Volume of cone = 1/3hπr²
= \(\frac{1}{3}\) × 11 × π × 3 × 3
= \(\frac{1}{1}\) × 11 × π × 3 × 1
= 33 × π
= 33 × \(\frac{22}{7}\)   (As π = \(\frac{22}{7}\))
= \(\frac{726}{7}\)
= 103.714 cubic ft.