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Question

# If the total surface area of a solid hemisphere is 462 cm2, then find its volume. [CBSE 2014]

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Solution

## $\mathrm{As},\mathrm{the}\mathrm{total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{solid}\mathrm{hemisphere}=462{\mathrm{cm}}^{2}\phantom{\rule{0ex}{0ex}}⇒3\mathrm{\pi }{r}^{2}=462\phantom{\rule{0ex}{0ex}}⇒3×\frac{22}{7}×{r}^{2}=462\phantom{\rule{0ex}{0ex}}⇒{r}^{2}=\frac{462×7}{3×22}\phantom{\rule{0ex}{0ex}}⇒{r}^{2}=49\phantom{\rule{0ex}{0ex}}⇒{r}^{2}=\sqrt{49}\phantom{\rule{0ex}{0ex}}⇒r=7\mathrm{cm}$ $\mathrm{Now},\mathrm{the}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{solid}\mathrm{hemisphere}=\frac{2}{3}\mathrm{\pi }{r}^{3}\phantom{\rule{0ex}{0ex}}=\frac{2}{3}×\frac{22}{7}×7×7×7\phantom{\rule{0ex}{0ex}}=\frac{2156}{3}{\mathrm{cm}}^{3}\phantom{\rule{0ex}{0ex}}=718\frac{2}{3}{\mathrm{cm}}^{3}$ = 718.67 cm3

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