How to Find the Volume of a Frustum of a Right Pyramid

Written by chance e. gartneer
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How to Find the Volume of a Frustum of a Right Pyramid
A pyramid's frustum robs it of its point. (Ablestock.com/AbleStock.com/Getty Images)

Finding the volume of a pyramidal frustum means finding just a part of pyramid's volume. If the pyramid's top point, known as its apex or common vertex, is directly over the centre of its base, the pyramid is termed a right pyramid. When a portion of a right pyramid's top is removed that leaves an upper base that is parallel to the pyramid's lower base, the resultant solid is called a right pyramidal frustum. You can find a right pyramid frustum's volume through the areas of its two bases and the height, or distance, between them.

Skill level:
Moderately Easy

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Things you need

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Instructions

  1. 1

    Calculate the bottom and top bases' areas. For this example, let the bottom base be a square with a side length of 4 units and the top base be a square with a side length of 2 units --- the area of the bottom base is 16 square units and the area of the top base is 4 square units.

  2. 2

    Multiply the two base areas, then find their product's square root. In this example, 4 multiplied by 16 results in 64, and the square root of 64 is 8 square units.

  3. 3

    Sum the areas from Step 1 with the square root from Step 2. In this example, 16, 4 and 8 square units added together equal 28 square units.

  4. 4

    Multiply the sum from Step 3 with the height between the two bases. In this example, let the height be 6 units --- multiplying 6 units by 28 square units results in 768 cubic units.

  5. 5

    Divide the product from Step 4 by 3. Concluding this example, 768 cubic units divided by 3 results in 256 cubic units.

Tips and warnings

  • A pyramidal frustum's volume can also be calculated by subtracting the volume of the part removed from the volume of the original pyramid.

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