SSC CHSL 2024 PYQ — Question 60

The correct answer is option 3 i.e. $\frac{125}{216}$.

Given that

The surface areas of the two spheres are in the ratio 25 : 36.

The surface area of the sphere = 4 π r²

The volume of the sphere V = 4/3 π r³,

where r is the radius of the sphere

⇒  4 π r₁²/ 4 π r₂² = 25/36

⇒ r₁/r₂ = 5/6

Hence, the ratio of the volumes = (r₁/r₂)³ = (5/6)³ = 125/216