Question

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Q). The volume of a hemisphere is $2425\frac{1}{2}c{m}^3$. Find its curved surface area.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{r}\mathrm{be}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{hemisphere}. \\ \mathrm{Volume}\mathrm{of}\mathrm{hemisphere}=2425\frac{1}{2}{\mathrm{cm}}^3 \\ \Rightarrow \frac{2}{3}{\mathrm{\pi r}}^3=\frac{4851}{2} \\ \Rightarrow \frac{2}{3}\times \frac{22}{7}\times {\mathrm{r}}^3=\frac{4851}{2} \\ \Rightarrow {\mathrm{r}}^3=\frac{4851\times 21}{88}=\frac{441\times 21}{8} \\ \Rightarrow \mathrm{r}=\frac{21}{2} \\ \Rightarrow \mathrm{r}=10.5\mathrm{cm} \\ \mathrm{Now},\mathrm{CSA}=2{\mathrm{\pi r}}^2 \\ =2\times \frac{22}{7}\times 10.5\times 10.5 \\ =693{\mathrm{cm}}^2 \end{gathered}$$