SSC CPO 2024 PYQ — Question 149

The correct answer is Option 1 i.e. 27 : 343.

Given that

surface areas of the two spheres are in the ratio = 9:49

Let the radius of the two spheres be r and R 

Surface area of sphere = 4πr²

Volume of sphere = $\frac{4}{3}$πr³

According to the question

4πr² : 4πR² = 9 :49

⇒ r² :R² = 9 : 49

⇒ $\frac{r}{R}$ = $\frac{3}{7}$

Hence, $\frac{4}{3}$πr³ : $\frac{4}{3}$πR³ = 3³ :7³ = 27 : 343

Hence, the ratio of their volumes is 27 : 343.