Question

A sphere and a hemisphere have the same volume the ratio of their curved surface area is

Answer 1

Let radius of sphere be a and that of hemisphere be b. Given,
$\frac{4}{3} \pi {a}^{3} = \frac{2}{3} \pi {b}^{3} \\ \frac{a}{b} = \sqrt[3]{ \frac{1}{2} } \\ ratio \: of \: curved \: surface \: area \\ = \frac{4\pi {a}^{2} }{2\pi {b}^{2} } = 2 \frac{ {a}^{2} }{ {b}^{2} } = 2 \times {( \frac{1}{2} )}^{ \frac{2}{3} } = {2}^{ \frac{1}{3} } \\ = \sqrt[3]{2}$