Management Aptitude Test Dec 2019 Paper

Question : 107 of 200

Marks: +1, -0

If the ratio of the volume of two cones is 1: 6 and the ratio of the radii of their bases is 1: 2 , then the ratio of their height will be

Solution:

Let the volume of cones

V_{1}, V_{2},

radii

R_{1}, R_{2}

and height

H_{1}, H_{2},

respectively.

{V_{1}}/{V_{2}}={1}/{6}

and

{R_{1}}/{R_{2}}={1}/{2}

Then,

{{1}/{3} \πR_{1}^{2} H_{1}}/{{1}/{3} \πR_{2}^{2} H_{2}}={1}/{6}

⇒({R_{1}}/{R_{2}})^{2} × ({H_{1}}/{H_{2}})={1}/{6}

⇒({1}/{2})^{2} × ({H_{1}}/{H_{2}})={1}/{6}

∴{H_{1}}/{H_{2}}={4}/{6}={2}/{3}

Hence, the required ratio

=2: 3

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