Composite Volume Basics

  • 9th Grade
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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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Quizzes Created: 8157 | Total Attempts: 9,569,759
| Attempts: 12 | Questions: 20 | Updated: Jan 19, 2026
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1) A cylinder with a radius 4 cm, height 10 cm has a cone of radius 4 cm, height 6 cm placed on top. Find the approximate total volume.

Explanation

Cylinder with a cone on top

Radius = 4 cm, cylinder height = 10 cm, cone height = 6 cm

Volume = (3.14 × 4 × 4 × 10) + (1 ÷ 3 × 3.14 × 4 × 4 × 6)

= 502.4 + 100.8 = 603.2

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About This Quiz
Composite Volume Basics - Quiz

Are you ready to see how big 3D shapes can be when we build them from parts? In this quiz, you’ll stack and combine shapes like cubes, prisms, cylinders, cones, and hemispheres to find total volume. You’ll also handle cut-outs (like drilling a hole) by subtracting volumes. Step by step,... see moreyou’ll use the right formulas and round when π appears.
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2) A rectangular prism with dimensions of 8 m 6 m 4 has a triangular prism with a height of 3 placed on top of its base 8 m 4. Find the total volume.

Explanation

Rectangular prism with a triangular prism on top

Prism volume = 8 × 6 × 4 = 192

Triangular prism = 0.5 × 8 × 3 × 4 = 48

Total = 192 + 48 = 240

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3) A silo is shaped like a cylinder of radius 6 m and height 12 m with a hemisphere of radius 6 m on top. Find the total volume.

Explanation

Cylinder with a hemisphere on top

Cylinder = 3.14 × 6 × 6 × 12 = 1357.4

Hemisphere = 2 ÷ 3 × 3.14 × 6 × 6 × 6 = 452.2

Total = 1809.6

Submit
4) A cone (radius 4 cm, height 9 cm) sits on top of a cylinder (radius 4 cm, height 12 cm). Find the total volume.

Explanation

Cone on top of a cylinder

Cylinder = 3.14 × 4 × 4 × 12 = 603.2

Cone = 1 ÷ 3 × 3.14 × 4 × 4 × 9 = 150.8

Total = 754

Submit
5) A cone of radius 3 cm and height 9 cm is cut from the top of a cylinder of radius 3 cm and height 9 cm. What is the remaining volume?

Explanation

Cylinder with a cone cut out

Cylinder = 3.14 × 3 × 3 × 9 = 254.3

Cone = 1 ÷ 3 × 3.14 × 3 × 3 × 9 = 84.8

Remaining = 254.3 - 84.8 = 169.5

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6) A dome is made of a cylinder (radius 10 m, height 15 m) with a hemisphere on top. Find the total volume.

Explanation

Cylinder with a hemisphere on top

Cylinder = 3.14 × 10 × 10 × 15 = 4710

Hemisphere = 2 ÷ 3 × 3.14 × 10 × 10 × 10 = 2093.3

Total = 6803.3

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7) A triangular prism (base 12 cm, height 8 cm, length 10 cm) is joined to a cube of side 10 cm. Find the total volume.

Explanation

Triangular prism with a cube

Triangular prism = 0.5 × 12 × 8 × 10 = 480

Cube = 10 × 10 × 10 = 1000

Total = 1480

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8) A cylinder of radius 2 cm and height 10 cm is combined with a cone of radius 2 cm and height 4 cm. Find the total volume.

Explanation

Cylinder with a cone

Cylinder = 3.14 × 2 × 2 × 10 = 125.6

Cone = 1 ÷ 3 × 3.14 × 2 × 2 × 4 = 16.8

Total = 142.4

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9) A cube with a side length of 6 cm has a hemisphere of radius 3 cm on top. Find the approximate total volume.

Explanation

Cube with a hemisphere on top

Cube side = 6 cm, hemisphere radius = 3 cm

Volume = (6 × 6 × 6) + (2 ÷ 3 × 3.14 × 3 × 3 × 3)

= 216 + 56.5 = 272.5

Submit
10) A sphere of radius 5 m is cut in half. What is the approximate volume of one half?

Explanation

Half of a sphere

Radius = 5 m

Volume = 0.5 × (4 ÷ 3 × 3.14 × 5 × 5 × 5)

= 0.5 × 523.6 = 261.8

Submit
11) A rectangular prism with dimensions of 5 m 5 m 10 has a pyramid with a height of 6 placed on top of its 5 m 5 base. Find the total volume.

Explanation

Rectangular prism with a pyramid on top

Prism = 5 × 5 × 10 = 250

Pyramid = 1 ÷ 3 × 5 × 5 × 6 = 50

Total = 300

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12) A cylinder of radius 7 cm and height 14 cm is combined with a hemisphere of radius 7 cm. Find the total volume.

Explanation

Cylinder with a hemisphere

Cylinder = 3.14 × 7 × 7 × 14 = 2156.7

Hemisphere = 2 ÷ 3 × 3.14 × 7 × 7 × 7 = 716.8

Total = 2873.5

Submit
13) A rectangular prism with dimensions of 12 m 10 m 6 has a half-cylinder of radius 5, length 10 placed on its top. Find the total volume.

Explanation

Rectangular prism with a half-cylinder on top

Prism = 12 × 10 × 6 = 720

Half-cylinder = 0.5 × 3.14 × 5 × 5 × 10 = 392.7

Total = 1112.7

Submit
14) A storage bin is a cube of side 8 m with a pyramid on top, base 8 m 8, height 6. Find the total volume.

Explanation

Cube with a pyramid on top

Cube = 8 × 8 × 8 = 512

Pyramid = 1 ÷ 3 × 8 × 8 × 6 = 128

Total = 640

Submit
15) A cube with side lengths of 5 is attached to a cone with a radius of 2.5 and a height of 6. Find the total volume.

Explanation

Cube with a cone attached

Cube = 5 × 5 × 5 = 125

Cone = 1 ÷ 3 × 3.14 × 2.5 × 2.5 × 6 = 39.3

Total = 164.3

Submit
16) A cylinder (radius 3 cm, height 12 cm) is filled with water. A cone (radius 3 cm, height 12 cm) is submerged inside. What is the remaining volume of water?

Explanation

Cylinder filled with water, cone removed

Cylinder = 3.14 × 3 × 3 × 12 = 339.1

Cone = 1 ÷ 3 × 3.14 × 3 × 3 × 12 = 113.0

Remaining = 339.1 - 113.0 = 226.1

Submit
17) An ice cream scoop (radius 3 cm) is placed on top of a cone (radius 3 cm, height 8 cm). Find the total volume.

Explanation

Ice cream scoop (half-sphere) on cone

Half-sphere = 2 ÷ 3 × 3.14 × 3 × 3 × 3 = 56.5

Cone = 1 ÷ 3 × 3.14 × 3 × 3 × 8 = 75.4

Total = 131.9

Submit
18) A rectangular prism with dimensions of 10 m 8 m 5 is attached to a half-sphere of radius 4. Find the total volume.

Explanation

Rectangular prism with a half-sphere

Prism = 10 × 8 × 5 = 400

Half-sphere = 2 ÷ 3 × 3.14 × 4 × 4 × 4 = 134.0

Total = 534.6

Submit
19) A cube with side lengths of 10 has a cylindrical hole drilled through with a radius of 2 and a height 10. Find the remaining volume.

Explanation

Cube with a cylindrical hole

Cube = 10 × 10 × 10 = 1000

Cylinder hole = 3.14 × 2 × 2 × 10 = 125.6

Remaining = 1000 - 125.6 = 874.4

Submit
20) A cone of radius 6 cm and height 12 cm is placed inside a cylinder of the same size. Find the volume of empty space.

Explanation

Cone inside a cylinder of the same size

Cylinder = 3.14 × 6 × 6 × 12 = 1356.5

Cone = 1 ÷ 3 × 3.14 × 6 × 6 × 12 = 452.2

Empty space = 1356.5 - 452.2 = 904.3

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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A cylinder with a radius 4 cm, height 10 cm has a cone of radius 4 cm,...
A rectangular prism with dimensions of 8 m 6 m 4 has a triangular...
A silo is shaped like a cylinder of radius 6 m and height 12 m with a...
A cone (radius 4 cm, height 9 cm) sits on top of a cylinder (radius 4...
A cone of radius 3 cm and height 9 cm is cut from the top of a...
A dome is made of a cylinder (radius 10 m, height 15 m) with a...
A triangular prism (base 12 cm, height 8 cm, length 10 cm) is joined...
A cylinder of radius 2 cm and height 10 cm is combined with a cone of...
A cube with a side length of 6 cm has a hemisphere of radius 3 cm on...
A sphere of radius 5 m is cut in half. What is the approximate volume...
A rectangular prism with dimensions of 5 m 5 m 10 has a pyramid with a...
A cylinder of radius 7 cm and height 14 cm is combined with a...
A rectangular prism with dimensions of 12 m 10 m 6 has a half-cylinder...
A storage bin is a cube of side 8 m with a pyramid on top, base 8 m 8,...
A cube with side lengths of 5 is attached to a cone with a radius of...
A cylinder (radius 3 cm, height 12 cm) is filled with water. A cone...
An ice cream scoop (radius 3 cm) is placed on top of a cone (radius 3...
A rectangular prism with dimensions of 10 m 8 m 5 is attached to a...
A cube with side lengths of 10 has a cylindrical hole drilled through...
A cone of radius 6 cm and height 12 cm is placed inside a cylinder of...
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