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SSC GD 2023 PYQ — Question 50

SSC GD Constable (English) - 10 Jan 2023 - Shift 3 • Quantitative Aptitude • Q50

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The volumes of two cones are in the ratio of 3 : 2 and their radii are in the ratio 3 : 4. The ratio of their heights is:

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 8:3

Ratio of volumes of two cones = 3 : 2

Ratio of radii of the two cones = 3 : 4

The volume of cone = (1/3)πr2h

Let x be a common factor. So, the ratio of their radii is 3x : 4x.

The volume of the first cone, V1 = (1/3)π(3x)2h1 = (1/3)π9x2h1

The volume of the second cone, V2 = (1/3)π(4x)2h2 = (1/3)π16x2h2

The ratio of volumes of the two cones = 3 : 2

V1/V2 = 3/2

9x​2h1/16x​2h2 = 3/2

h1/h2 = 48/18

h1/h2 = 8/3