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ISEE Upper Level
Mathematics Achievement

Volume of the Frustum of a Cone

Very Hard Geometry Solid Geometry

Consider a right circular cone with a base radius of $r$ and a height of $h$. A plane cuts the cone parallel to its base at a height of $k$ (where $0 < k < h$), resulting in a smaller cone on top. If the height of the smaller cone created by this cut is $h_k = h - k$, find the volume of the section of the cone that is removed (the frustum) in terms of $r$, $h$, and $k$. The volume $V$ of a cone is given by the formula:

$$ V = rac{1}{3} imes ext{Base Area} imes ext{Height} = rac{1}{3} imes rac{22}{7} r^2 h $$

Based on the information given, which of the following represents the volume of the frustum?

Hint

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