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SSC Selection Post 2024 PYQ — Question 51

SSC Selection Post - Matriculation Level - 26 June 2024 - Shift 1 • Quantitative Aptitude • Q51

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If the surface areas of two spheres are in the ratio of 9 : 49, then the ratio of their volumes is:

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Correct answer: C

Explanation

The correct answer is Option 3 i.e. 27 : 343

The formula for the surface area of a sphere (S) = 4πr2 

The formula for the volume of a sphere is (V) = 4/3πr3

 If the surface areas are in the ratio 9 : 49, then (r1/r2)2 = 9/49

r1/r2 = 3/7

Ratio of volumes = (r1r2)3=(37)3\left( \frac{r_1}{r_2} \right)^3 = \left( \frac{3}{7} \right)^3 = 27/343