SSC CPO SI and ASI 2013 Paper

Question : 139 of 200

Marks: +1, -0

If the volumes of two right circular cones are in the ratio 4 : 1, and their diameters are in the ratio 5 : 4, then the ratio of their heights is

Solution:

(3) Let the volumes of two cones be V

_{1}

and V

_{2}

, diameters be d

_{1}

and d

_{2}

, and heights be h

_{1}

and h

_{2}

. So,

{v_{1}}/{V_{2}}= {d_{1}^{2} h_{1}}/{d_{2}^{2} h_{2}}

⇒{4}/{1}= {25 ×{h}_{1}}/{16 ×{h}_{2}}

⇒{ {h}_{1}}/{ {h}_{2}}= {64}/{25}

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