Students can use the **Spectrum Math Grade 8 Answer Key** **Chapter 5 Lesson 5.12 Volume: Spheres** 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 = \(\frac{4}{3}\)πr^{3}. 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.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

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 = \(\frac{4}{3}\)πr(3.5)^{3} = \(\frac{4}{3}\)π(42.875) = 179.5 cubic meters

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

Question 1.

a.

V = ____ m^{3}

Answer: 267.95m^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

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 = \(\frac{4}{3}\)πr(4)^{3} = 267.94666 m^{3}= 267.95m^{3}

b.

V = ____ ft.^{3}

Answer: 373.03 ft.^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

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 = \(\frac{4}{3}\)πr(4.5)^{3} = 373.032 ft.^{3}= 373.03 ft.^{3}

c.

V = ____ cm^{3}

Answer: 1766.25 cm^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

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 = \(\frac{4}{3}\)πr(7.5)^{3} = 1766.25 cm^{3}

Question 2.

a.

V = ____ in.^{3}

Answer: 2143.57 in.^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

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 = \(\frac{4}{3}\)πr(8)^{3} = 2143.57333 in.^{3} = 2143.57 in.^{3}

b.

V = ____ km^{3}

Answer: 523.33 km^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

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 = \(\frac{4}{3}\)πr(5)^{3} = 523.333 km^{3}= 523.33 km^{3}

c.

V = ____ m^{3}

Answer: 4186.67 m^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

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 = \(\frac{4}{3}\)πr(10)^{3} = 4186.66666 m^{3}= 4168.67 m^{3}

Question 3.

a.

V = ____ ft.^{3}

Answer: 904.32 ft.^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

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 = \(\frac{4}{3}\)πr(6)^{3} = 904.32 ft.^{3}

b.

V = ____ cm^{3}

Answer: 1436.0266 cm^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

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 = \(\frac{4}{3}\)πr(7)^{3} = 1436.0266 cm^{3}= 1436.03 cm^{3}

c.

V = ____ in.^{3}

Answer: 113.04 in.^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

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 = \(\frac{4}{3}\)πr(3)^{3} = 113.04 in.^{3}

**Find the volume of each sphere. Use 3.14 to represent π. Round answers to the nearest hundredth.**

Question 1.

a.

V = ____ m^{3}

Answer: 523.33 m^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

Given, r = 5m

V = \(\frac{4}{3}\)πr(5)^{3} = 523.3333 m^{3}= 523.33 m^{3}

b.

V = ____ cm^{3}

Answer: 4186.67cm^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

Given, r = 10 cm

V = \(\frac{4}{3}\)πr(10)^{3} = 4186.6666 cm^{3}= 4186.67 cm^{3}

c.

V = ____ yd.^{3}

Answer: 904.32 yd.^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

Given, r = 6 yd.

V = \(\frac{4}{3}\)πr(6)^{3} = 904.32 yd.^{3}

Question 2.

a.

V = ____ ft.^{3}

Answer: 267.95 ft.^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

Given, r = 4 ft.

V = \(\frac{4}{3}\)πr(4)^{3} = 267.94666 ft.^{3}= 267.95 ft.^{3}

b.

V = ____ in.^{3}

Answer: 4.19 in.^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

Given, r = 1 in.

V = \(\frac{4}{3}\)πr(1)^{3} = 4.18666 in.^{3}= 4.19 in.^{3}

c.

V = ____ m^{3}

Answer: 1436.03 m^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

Given, r = 7 m

V = \(\frac{4}{3}\)πr(7)^{3} = 1436.02666 m^{3}= 1436.03m^{3}

Question 3.

a.

V = ____ cm^{3}

Answer: 2143.57333 cm^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

Given, r = 8 cm

V = \(\frac{4}{3}\)πr(8)^{3} = 2143.57333 cm^{3}= 2143.57 cm^{3}

b.

V = ____ mi.^{3}

Answer: 33.49 mi.^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

Given, r = 2 mi.

V = \(\frac{4}{3}\)πr(2)^{3} = 33.4933 mi.^{3}= 33.49 mi.^{3}

c.

V = ____ cm^{3}

Answer: 3052.08 cm^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

Given, r = 9 cm

V = \(\frac{4}{3}\)πr(9)^{3} = 3052.08 cm^{3}

Question 4.

a.

V = ____ ft.^{3}

Answer: 113.04 ft.^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

Given, r = 3 ft.

V = \(\frac{4}{3}\)πr(3)^{3} = 113.04 ft.^{3}

b.

V = ____ in.^{3}

Answer: 7234.56 in.^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

Given, r = 12 in.

V = \(\frac{4}{3}\)πr(12)^{3} = 7234.56 in.^{3}

c.

V = ____ cm^{3}

Answer: 14130 cm^{3}

Volume is the amount of space a three-dimensional figure occupies. The volume of a sphere is calculated as V = \(\frac{4}{3}\)πr^{3}.

\(\frac{4}{3}\)πr^{3} Volume is given in cubic units or units^{3}.

Given, r = 15 cm

V = \(\frac{4}{3}\)πr(15)^{3} = 14130 cm^{3}