A solid cone is cut by a plane parallel to its base passing through the midpoint of its axis, so that a small cone is separated from the frustum below it. Find the ratio of the volume of the small cone to the volume of the frustum.

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Accepted Answer

1:7. The small cone is similar to the whole cone with linear ratio 1 : 2, so its volume is (1/2)³ = 1/8 of the whole. Taking the whole cone as 8 parts, the small cone is 1 part and the frustum is 8 − 1 = 7 parts. Ratio = 1 : 7.

A solid cone is cut by a plane parallel to its base passing through the midpoint of its axis, so that a small cone is separated from the frustum below it. Find the ratio of the volume of the small cone to the volume of the frustum.

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