Question

A cone of radius 4 cm with a slant height of 12 cm was sliced horizontally, resulting into a smaller cone (upper portion) and a frustum (lower portion). If the ratio of the curved surface area of the upper smaller cone and the lower frustum is 1:2, what will be the slant height of the frustum?

Accepted Answer

D. CSA of upper cone : CSA of frustum = $1:2 \implies$ CSA of upper cone : CSA of full cone = $1:3$. Since CSA $\propto l^2$, $\left(\frac{l_{	ext{small}}}{12}ight)^2 = \frac{1}{3} \implies l_{	ext{small}} = \frac{12}{\sqrt{3}} = 4\sqrt{3}$. Slant height of frustum = $12 - l_{	ext{small}} = 12 - 4\sqrt{3}$.

Frustum of a Cone

Explanation

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