| The volume of a solid hemisphere is \[19404\,\,c{{m}^{3}}.\] Its total surface area is [SSC (CGL) 2012] |
A) \[4158\,\,c{{m}^{2}}\]
B) \[2858\,\,c{{m}^{2}}\]
C) \[1738\,\,c{{m}^{2}}\]
D) \[2038\,\,c{{m}^{2}}\]
Correct Answer: A
Solution :
| Volume of hemisphere = 19404 |
| \[\frac{2}{3}\pi {{r}^{3}}=19404\] |
| \[\Rightarrow \] \[\frac{2}{3}\times \frac{22}{7}\times {{r}^{3}}=19404\] |
| \[\Rightarrow \] \[{{r}^{3}}=\frac{19404\times 3\times 7}{2\times 22}=9261\] |
| \[r=\sqrt[3]{21\times 21\times 21}=21\,\,cm\] |
| \[\therefore \]Total surface area \[=3\pi {{r}^{2}}\] |
| \[=3\times \frac{22}{7}\times 21\times 21=4158\,\,c{{m}^{2}}\] |
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