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Frustum of a Cone

XAT 2018 · Quantitative Ability & Data Interpretation · Medium · Quantitative Aptitude

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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?

  1. A.

    12−312 - \sqrt{3}

  2. B.

    12−2312 - 2\sqrt{3}

  3. C.

    12−3312 - 3\sqrt{3}

  4. D.

    12−4312 - 4\sqrt{3}

  5. E.

    None of the above

Answer

D

Explanation

CSA of upper cone : CSA of frustum = 1:2  ⟹  1:2 \implies CSA of upper cone : CSA of full cone = 1:31:3. Since CSA ∝l2\propto l^2, (lsmall12)2=13  ⟹  lsmall=123=43\left(\frac{l_{\text{small}}}{12}\right)^2 = \frac{1}{3} \implies l_{\text{small}} = \frac{12}{\sqrt{3}} = 4\sqrt{3}. Slant height of frustum = 12−lsmall=12−4312 - l_{\text{small}} = 12 - 4\sqrt{3}.

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