If the curved surface area of a sphere is \(S\) square units and its volume is \(V\) cubic units, then determine the relationship between \(S\) and \(V\).

Q.If the curved surface area of a sphere is \(S\) square units and its volume is \(V\) cubic units, then determine the relationship between \(S\) and \(V\).

Let the radius of the sphere be \(r\) units. ∴ Curved surface area of the sphere, \(S = 4πr^2\) square units And volume of the sphere, \(V = \frac{4}{3}πr^3\) cubic units Now, \(\frac{S^3}{V^2} = \frac{(4πr^2)^3}{\left(\frac{4}{3}πr^3\right)^2}\) \(= \frac{64π^3r^6}{\frac{16}{9}π^2r^6} = 4 × 9π = 36π\) ∴ \(\frac{S^3}{V^2} = 36π\)