If the curved surface area of a solid sphere is \(s\) and its volume is \(v\), then what is the value of \(\frac{s^3}{v^2}\)?

Q.If the curved surface area of a solid sphere is \(s\) and its volume is \(v\), then what is the value of \(\frac{s^3}{v^2}\)?

Let the radius of the sphere be \(r\).
\(\therefore s = 4\pi r^2\)
And \(v = \cfrac{4}{3}\pi r^3\)

\(\therefore \cfrac{s^3}{v^2} = \cfrac{(4\pi r^2)^3}{(\cfrac{4}{3}\pi r^3)^2}\)
\(= \cfrac{64\pi^3 r^6}{\cfrac{16}{9}\pi^2 r^6}\)
\(= \cfrac{64\pi \times 9}{16} = 36\pi\)