SSC CPO 2023 PYQ — Question 145

The correct answer is option 3 i.e. 3$\sqrt{3}$ : 4.

Given that

A sphere and another solid hemisphere have the same surface area

Volume of a sphere V = 4/3 π R³

Volume of a solid hemisphere = 2/3 π r³

According to the question

Surface area of a sphere = Surface area of a hemisphere

4π R² = 3π r²

R/r = $\sqrt{3}$/2

Volume of a sphere/Volume of a solid hemisphere = (4/3 π R³)/(2/3 π r³)

= 2(R/r)³ 

= 2($\sqrt{3}$/2)³ 

= 3$\sqrt{3}$ /4

Hence, The ratio of their volumes is 3$\sqrt{3}$ : 4