Volume of Truncated Cones & Pyramids Worksheet
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Examples, solutions, videos, and worksheets to help Grade 8 students learn that a truncated cone or pyramid is the solid obtained by removing the top portion of a cone or a pyramid above a plane parallel to its base and to find the volume of truncated cones and volume of truncated pyramids using similar triangles.
How to find the volume of truncated cones & pyramids?
To find the volume of a truncated cone using similar triangles, we rely on the fact that a truncated cone can be thought of as a cone with the top section “cut off.” This top portion is a smaller cone that is similar to the original larger cone. By using properties of similar triangles, we can relate the dimensions of the smaller and larger cones, and subtract the volume of the smaller cone from the larger cone to find the volume of the frustum (truncated cone).
Steps to Solve the Volume of a Truncated Cone Using Similar Triangles:
- Identify the dimensions of the truncated cone:
𝑟1: radius of the larger base,
𝑟2: radius of the smaller base,
h: height of the frustum (truncated cone),
𝐻: the height of the original larger cone (if it were complete), which includes both the height of the frustum and the height of the smaller cone. - Use similar triangles to relate the height of the larger cone 𝐻 and the height of the smaller cone h to the radii of the bases.
- Subtract the volume of the smaller cone from the volume of the larger cone to get the volume of the truncated cone.
This following figure shows how to find the volume of a truncated cone (frustum) pictorially:
Have a look at this video if you need to review how to the volume of a truncated cone.
Click on the following worksheet to get a printable pdf document.
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More Volume of Truncated Cone Worksheets
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(Answers on the second page.)
Volume of Truncated Cone Worksheet #1
Volume of Truncated Cone Worksheet #2
Volume of Truncated Cone Worksheet #3
Volume of Truncated Cone Worksheet #4
Volume of Truncated Cone Worksheet #5
Volume of Truncated Cone Worksheet #6
Volume of Truncated Cone Worksheet #7
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Volume of Truncated Cones & Pyramids
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