| Weight of a solid metallic sphere of radius 4 cm is 4 kg. The weight of a hollow sphere made with same metal, whose outer diameter is 16 cm and inner diameter is 12 cm, is |
A) 20.5 kg
B) 15.5 kg
C) 16.5 kg
D) 18.5 kg
Correct Answer: D
Solution :
| Volume of solid sphere of radius \[4\,\,cm=\frac{4}{3}\pi \,\,{{(4)}^{3}}\,\,cm\] |
| Volume of hollow sphere \[=\frac{4}{3}\pi [{{(8)}^{3}}-{{(6)}^{3}}]\,\,c{{m}^{3}}\] |
| \[\because \]Weight of \[\frac{4}{3}\pi \,\,{{(4)}^{3}}c{{m}^{3}}=4\,\,kg\] |
| \[\therefore \]Weight of \[\frac{4}{3}\pi \,\,[{{(8)}^{3}}-{{(6)}^{3}}]\,\,c{{m}^{3}}\] |
| \[=\frac{4}{\frac{4}{3}\pi {{(4)}^{3}}}\cdot \frac{4}{3}\pi [{{(8)}^{3}}-{{(6)}^{3}}]\] |
| \[=\frac{4\,\,(512-216)}{{{4}^{3}}}=18.5\,\,kg\] |
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