SSC Selection Post 2024 PYQ — Question 61

The correct answer is Option 1 i.e. ${{\sqrt6:}}{{\sqrtπ}}$.

The surface area of cube = 6 a²

The surface area of sphere = 4π r²

Volume of a cube = a³

Volume of sphere = 4π r³/3

6a² = 4 π r²

⇒ a² = 4π r²/6

⇒ a²/r² = 4π /6

⇒ a/r = 2 √π /√6 

Assuming, a = 2√π , r = √6

Volume of a cube = (2 √π)³

⇒  8π√π 

Volume of sphere = 4 π × (√6)³/3  

⇒ 4π × 6 √ 6/3 = 4 π × 2 √6

⇒ 8π √6  

The ratio of the volume of sphere and cube = 8π √6 ÷  8π √π

⇒ √6/√π