A sphere and a hemisphere have the same volume the ratio of their curved surface area is
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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}](https://tex.z-dn.net/?f=+%5Cfrac%7B4%7D%7B3%7D+%5Cpi+%7Ba%7D%5E%7B3%7D++%3D++%5Cfrac%7B2%7D%7B3%7D+%5Cpi+%7Bb%7D%5E%7B3%7D++%5C%5C++%5Cfrac%7Ba%7D%7Bb%7D++%3D++%5Csqrt%5B3%5D%7B+%5Cfrac%7B1%7D%7B2%7D+%7D++%5C%5C+ratio+%5C%3A+of+%5C%3A+curved+%5C%3A+surface+%5C%3A+area+%5C%5C++%3D++%5Cfrac%7B4%5Cpi+%7Ba%7D%5E%7B2%7D+%7D%7B2%5Cpi+%7Bb%7D%5E%7B2%7D+%7D++%3D+2+%5Cfrac%7B+%7Ba%7D%5E%7B2%7D+%7D%7B+%7Bb%7D%5E%7B2%7D+%7D++%3D+2++%5Ctimes++%7B%28+%5Cfrac%7B1%7D%7B2%7D+%29%7D%5E%7B+%5Cfrac%7B2%7D%7B3%7D+%7D++%3D++%7B2%7D%5E%7B+%5Cfrac%7B1%7D%7B3%7D+%7D++%5C%5C++%3D++%5Csqrt%5B3%5D%7B2%7D+ "\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}")
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