If \(S\) is the curved surface area and \(V\) is the volume of a sphere, the value of \(\cfrac{S^3}{V^2}\) is –

Q.If \(S\) is the curved surface area and \(V\) is the volume of a sphere, the value of \(\cfrac{S^3}{V^2}\) is – (a) 4π (b) 12π (c) 36π (d) 72π

Answer: C

Let the radius of the sphere = \(r\) units.
∴ The curved surface area of the sphere \(S = 4πr^2\) square units,
and the volume of the sphere \(V = \cfrac{4}{3} πr^3\) cubic units.

∴ \(\cfrac{S^3}{V^2} = \cfrac{(4πr^2)^3}{(\cfrac{4}{3} πr^3)^2}\)
\(= \cfrac{64π^3 r^6}{\cfrac{16}{9} π^2 r^6} = 4 × 9π = 36π\).