Spectrum Math Grade 8 Chapter 5 Lesson 10 Answer Key Volume: Cylinders

Students can use the Spectrum Math Grade 8 Answer Key Chapter 5 Lesson 5.10 Volume: Cylinders as a quick guide to resolve any of their doubts.

Spectrum Math Grade 8 Chapter 5 Lesson 5.10 Volume: Cylinders Answers Key

Volume is the amount of space a three-dimensional figure occupies. You can calculate the volume of a cylinder by multiplying the area of the base by the height (Bh).
The area of the base is the area of the circle, πr², s0 volume can be found using the formula: V = πr²h

The volume is expressed in cubic units, or units³.
If r = 3 cm and h = 10 cm, what is the volume? Use 3.14 for π.
V = πr²h V = π(3² × 10) V = π × 90 V = 282.6 cm³

Find the volume of each cylinder. Use 3,14 for π. Remember that d = 2r. Round answers to the nearest hundredth.

Question 1.
a.

V = ____ in.³
Answer: 942 in.³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are r = 5 in. and h = 12 in.
Use 3.14 for π.
So, V = πr²h V = π(5² × 12) V = 942 in.³

b.

V = ____ ft.³
Answer: 502.4 ft.³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are r = 4 ft. and h = 10 ft.
Use 3.14 for π.
So, V = πr²h V = π(4² × 10) V = 502.4 ft.³

c.

V = ____ mm³
Answer: 1607.68 mm³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are d = 16mm so, r = d/2 = 16/2 = 8mm and h = 8 mm
Use 3.14 for π.
So, V = πr²h V = π(8² × 8) V = 1607.68 mm³

Question 2.
a.

V = ____ cm³
Answer: 678.24 cm³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are d = 12 cm so, r = d/2 = 12/2 = 6cm and h = 6 cm
Use 3.14 for π.
So, V = πr²h V = π(6² × 6) V = 678.24 cm³

b.

V = ____ in.³
Answer: 549.5 in.³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are r = 5 in. and h = 7 in.
Use 3.14 for π.
So, V = πr²h V = π(5² × 7) V = 549.5 in.³

c.

V = ____ m³
Answer: 1.1304 m³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are r = 0.6 m and h = 1 m
Use 3.14 for π.
So, V = πr²h V = π(0.6² × 1) V = 1.1304 m³

Question 3.
a.

V = ____ m³
Answer: 552.64 m³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are r = 4 m and h = 11 m.
Use 3.14 for π.
So, V = πr²h V = π(4² × 11) V = 552.64 m³

b.

V = ____ ft.³
Answer: 14.13 ft.³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are d = 3 ft. so, r = d/2 = 3/2 = 1.5 ft. and h = 2 ft.
Use 3.14 for π.
So, V = πr²h V = π(1.5² × 2) V = 14.13 ft.³

c.

V = ____ cm³
Answer: 1256 cm³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are d = 10 cm, so r = d/2 = 10/2 = 5 cm and h = 16 cm
Use 3.14 for π.
So, V = πr²h V = π(5² × 16) V = 1256 cm³

Find the volume of each cylinder. Use 3.14 for π. Round answers to the nearest hundredth.

Question 1.
a.

V = ____ in.³
Answer:  16076.80 in.³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are r = 16 in. and h = 20 in.
Use 3.14 for π.
So, V = πr²h V = π(16² × 20) V = 16076.80 in.³

b.

V = ____ cm³
Answer: 3538.78 cm³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are r = 16 in. and h = 20 in.
Use 3.14 for π.
So, V = πr²h V = π(16² × 20) V = 16076.80 in.³

c.

V = ____ ft.³
Answer: 747.76 7596 ft.³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are r = 6.3  ft. and h = 6 ft.
Use 3.14 for π.
So, V = πr²h V = π(6.3² × 6) V = 747.76 7596 ft.³

Question 2.
a.

V = ____ m³
Answer: 1582.56 m³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are d = 12m, so r = d/2 = 12/2 = 6m and h = 14m
Use 3.14 for π.
So, V = πr²h V = π(6² × 14) V = 1582.56 m³

b.

V = ____ mm³
Answer: 8440.32 mm³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are r = 8 mm and h = 42 mm
Use 3.14 for π.
So, V = πr²h V = π(8² × 42) V = 8440.32 mm³

c.

V = ____ in.³
Answer: 87.92 in.³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are r = 2 in. and h = 7 in.
Use 3.14 for π.
So, V = πr²h V = π(2² × 7) V = 87.92 in.³

Question 3.
a.

V = ____ mm³
Answer: 26660.01 mm³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are d = 23 mm, so r = d/2 = 23/2 = 11.5 mm and h = 64.2mm
Use 3.14 for π.
So, V = πr²h V = π(11.5² × 64.2) V = 26660.013 mm³ =2 6660.01 mm³

b.

V = ____ yd.³
Answer: 2034.72 yd.³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are r = 18 yd. and h = 2 yd.
Use 3.14 for π.
So, V = πr²h V = π(18² × 2) V = 2034.72 yd.³

c.

V = ____ cm³
Answer: 4876.92 cm³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are r = 8.6 cm and h = 21 cm
Use 3.14 for π.
So, V = πr²h V = π(8.6² × 21) V = 4876.9224 cm³= 4876.92 cm³

Question 4.
a.

V = ____ ft.³
Answer: 4710 ft.³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are r = 10 ft. and h = 15 ft.
Use 3.14 for π.
So, V = πr²h V = π(10² × 15) V = 4710 ft.³

b.

V = ____ cm³
Answer: 549.5 cm³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are r = 5 cm and h = 7 cm
Use 3.14 for π.
So, V = πr²h V = π(5² × 7) V = 549.5 cm³

c.

V = ____ m³
Answer: 452.16 m³
Volume is the amount of space a three-dimensional figure occupies. The volume of a cylinder by multiplying the area of the base by the height (Bh). The area of the base is the area of the circle, πr², so volume can be found using the formula: V = πr²h
The volume is expressed in cubic units, or units³.
The given values are r = 4 m and h = 9 m
Use 3.14 for π.
So, V = πr²h V = π(4² × 9) V = 452.16 m³