| If 64 identical small spheres are made out of a big sphere of diameter 8 cm, what is surface area of each small sphere? |
A) \[\pi \,\,c{{m}^{2}}\]
B) \[2\pi \,\,c{{m}^{2}}\]
C) \[4\pi \,\,c{{m}^{2}}\]
D) \[8\pi \,\,c{{m}^{2}}\]
Correct Answer: C
Solution :
| Volume of small spheres |
| \[=\frac{\text{Volume}\,\,\text{of}\,\,\text{bigger}\,\,\text{sphere}}{\text{Number}\,\,\text{of}\,\,\text{small}\,\,\text{sphere}}=\frac{\frac{4}{3}\pi {{(4)}^{3}}}{64}\] |
| \[=\frac{4}{3}\times \frac{\pi \times 4\times 4\times 4}{64}=\frac{4}{3}\pi c{{m}^{2}}\] |
| Let radius of small sphere be r'. |
| \[\therefore \]\[\frac{4}{3}\pi {{r}^{3}}=\frac{4}{3}\pi \]\[\Rightarrow \]\[r'=1\,\,cm\] |
| Now, surface area of small sphere \[=4\pi r{{'}^{2}}=4\pi \,\,c{{m}^{2}}\] |
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