Question

the ratio of surface area of a sphere and curved surface area of a hemisphere is 9:2 find ratio of their volumes​

Answer 1

Answer :-

Step by step explanation :-

Here we have ratio of surface area of a sphere and curved surface area of a hemisphere is 9:2.

Than,

$\frac{4\pi {r}^{2} }{3\pi {r}^{2} } = \frac{9}{2} \\ \\ \frac{4 {r}^{2} }{3 {r}^{2} } = \frac{9}{2} \\ \\ \frac{ {r}^{2} }{ {r}^{2} } = \frac{27}{8} \\ \\ \frac{r}{r} = \sqrt{ \frac{27}{8} } \\ \\ \frac{r}{r } = \sqrt{ \frac{9 \times 3}{4 \times 2} } \\ \\ \frac{r}{r} = \frac{3 \sqrt{3} }{2 \sqrt{2} }$

Ratio of volume :-

$= \frac{ \frac{4}{3} \pi {r}^{3} }{ \frac{2}{3} \pi {r}^{3} } \\ \\ = \frac{4 \times 3 \times r \times r \times r }{3 \times 2 \times r \times r \times r} \\ \\ = \frac{12 \times {(3 \sqrt{3}) }^{ 3} }{6 {(2 \sqrt{2} )}^{3} } \\ \\ = \frac{12 \times 3 \sqrt{3} }{6 \times 2 \sqrt{2} } \\ \\ = \frac{6 \sqrt{3} }{2 \sqrt{2} } \\ \\ = \frac{3 \sqrt{3} }{2}$

Answer is 3√3:2

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