# Spectrum Math Grade 8 Chapter 5 Lesson 12 Answer Key Volume: Spheres

Students can use the Spectrum Math Grade 8 Answer Key Chapter 5 Lesson 5.12 Volume: SpheresÂ as a quick guide to resolve any of their doubts.

## Spectrum Math Grade 8 Chapter 5 Lesson 5.12 Volume: Spheres Answers Key

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3. When the diameter of a sphere is known, it can be divided by 2 and then the formula for the volume of a sphere can be used.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
The radius of a sphere is half of its diameter. Find the radius, then calculate the volume.
r = $$\frac{1}{2}$$d = $$\frac{1}{2}$$(7) = $$\frac{7}{2}$$ = 3.5
V = $$\frac{4}{3}$$Ď€r(3.5)3 = $$\frac{4}{3}$$Ď€(42.875) = 179.5 cubic meters

Find the volume of each sphere. Use 3.1 4 to represent Ď€. Round answers to the nearest hundredth.

Question 1.
a.

V = ____ m3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, d = 8m
The radius of a sphere is half of its diameter. Find the radius, then calculate the volume.
r = $$\frac{1}{2}$$d = $$\frac{1}{2}$$(8) = 4
V = $$\frac{4}{3}$$Ď€r(4)3 =Â  267.94666 m3= 267.95m3

b.

V = ____ ft.3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, d = 9 ft.
The radius of a sphere is half of its diameter. Find the radius, then calculate the volume.
r = $$\frac{1}{2}$$d = $$\frac{1}{2}$$(9) = 4.5
V = $$\frac{4}{3}$$Ď€r(4.5)3 =Â  373.032 ft.3= 373.03 ft.3

c.

V = ____ cm3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, d = 15 cm
The radius of a sphere is half of its diameter. Find the radius, then calculate the volume.
r = $$\frac{1}{2}$$d = $$\frac{1}{2}$$(15) = 7.5
V = $$\frac{4}{3}$$Ď€r(7.5)3 = 1766.25 cm3

Question 2.
a.

V = ____ in.3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, d = 16 in.
The radius of a sphere is half of its diameter. Find the radius, then calculate the volume.
r = $$\frac{1}{2}$$d = $$\frac{1}{2}$$(16) = 8
V = $$\frac{4}{3}$$Ď€r(8)3 = 2143.57333 in.3 = 2143.57 in.3

b.

V = ____ km3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, d = 10 km
The radius of a sphere is half of its diameter. Find the radius, then calculate the volume.
r = $$\frac{1}{2}$$d = $$\frac{1}{2}$$(10) = 5 km
V = $$\frac{4}{3}$$Ď€r(5)3 = 523.333 km3= 523.33 km3

c.

V = ____ m3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, d = 20 m
The radius of a sphere is half of its diameter. Find the radius, then calculate the volume.
r = $$\frac{1}{2}$$d = $$\frac{1}{2}$$(20) = 10 m
V = $$\frac{4}{3}$$Ď€r(10)3 = 4186.66666 m3= 4168.67 m3

Question 3.
a.

V = ____ ft.3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, d = 12 ft.
The radius of a sphere is half of its diameter. Find the radius, then calculate the volume.
r = $$\frac{1}{2}$$d = $$\frac{1}{2}$$(12) = 6 ft.
V = $$\frac{4}{3}$$Ď€r(6)3 = 904.32 ft.3

b.

V = ____ cm3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, d = 14 cm
The radius of a sphere is half of its diameter. Find the radius, then calculate the volume.
r = $$\frac{1}{2}$$d = $$\frac{1}{2}$$(14) = 7 cm
V = $$\frac{4}{3}$$Ď€r(7)3 = 1436.0266 cm3= 1436.03 cm3

c.

V = ____ in.3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, d = 6 in.
The radius of a sphere is half of its diameter. Find the radius, then calculate the volume.
r = $$\frac{1}{2}$$d = $$\frac{1}{2}$$(6) = 3 in.
V = $$\frac{4}{3}$$Ď€r(3)3 = 113.04Â  in.3

Find the volume of each sphere. Use 3.14 to represent Ď€. Round answers to the nearest hundredth.

Question 1.
a.

V = ____ m3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, r = 5m
V = $$\frac{4}{3}$$Ď€r(5)3 = 523.3333 m3= 523.33 m3

b.

V = ____ cm3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, r = 10 cm
V = $$\frac{4}{3}$$Ď€r(10)3 = 4186.6666 cm3= 4186.67 cm3

c.

V = ____ yd.3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, r = 6 yd.
V = $$\frac{4}{3}$$Ď€r(6)3 = 904.32 yd.3

Question 2.
a.

V = ____ ft.3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, r = 4 ft.
V = $$\frac{4}{3}$$Ď€r(4)3 = 267.94666 ft.3= 267.95 ft.3

b.

V = ____ in.3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, r = 1 in.
V = $$\frac{4}{3}$$Ď€r(1)3 = 4.18666 in.3= 4.19 in.3

c.

V = ____ m3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, r = 7 m
V = $$\frac{4}{3}$$Ď€r(7)3 = 1436.02666 m3= 1436.03m3

Question 3.
a.

V = ____ cm3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, r = 8 cm
V = $$\frac{4}{3}$$Ď€r(8)3 = 2143.57333 cm3= 2143.57 cm3

b.

V = ____ mi.3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, r = 2 mi.
V = $$\frac{4}{3}$$Ď€r(2)3 = 33.4933 mi.3= 33.49 mi.3

c.

V = ____ cm3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, r = 9 cm
V = $$\frac{4}{3}$$Ď€r(9)3 = 3052.08 cm3

Question 4.
a.

V = ____ ft.3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, r = 3 ft.
V = $$\frac{4}{3}$$Ď€r(3)3 = 113.04 ft.3

b.

V = ____ in.3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
Given, r = 12 in.
V = $$\frac{4}{3}$$Ď€r(12)3 = 7234.56 in.3

c.

V = ____ cm3
Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = $$\frac{4}{3}$$Ď€r3.
$$\frac{4}{3}$$Ď€r3 Volume is given in cubic units or units3.
V = $$\frac{4}{3}$$Ď€r(15)3 = 14130 cm3