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A cone of base radius 9 cm and height 12 cm is sliced by a plane parallel to its base at a height of 4 cm above the vertex. Find the volume of the frustum that results.

1. 432 pi cm^3
2. 576 pi cm^3
3. 648 pi cm^3
4. 312 pi cm^3

Correct answer: 312 pi cm^3

Solution

The full cone has volume (1/3)pi(9^2)(12) = 324 pi. The small cone cut off (radius 3, height 4 by similar triangles) has volume (1/3)pi(3^2)(4) = 12 pi. Frustum = 324 pi - 12 pi = 312 pi cm^3.

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