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SSC CGL 2024 PYQ — Question 64

SSC CGL - 09 Sep 2024 - Shift 1 • Quantitative Aptitude • Q64

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The radii of the two cones are in the ratio of 2 : 5 and their volumes are in the ratio of 3 : 5. What is the ratio of their heights?

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 15 : 4.

The volume of the cone = 13πr2h{1\over 3} \pi r^2h

According to the given question,

V1V2=13πr12h113πr22h2{V_1 \over V_2} = {{{1\over 3}\pi r_1^2 h_1} \over {1\over 3}\pi r_2^2h_2}

⇒ 35=22h152h2{3 \over 5} = {{2^2 h_1} \over {5^2h_2}}

⇒ 35=4h125h2{3 \over 5} = {{4 h_1} \over {25h_2}}

⇒ h1h2=154{h_1 \over h_2} = {15 \over 4}