A) \[\frac{1}{2}{{\pi }^{3}}{{a}^{2}}\]
B) \[{{\pi }^{3}}{{a}^{2}}\]
C) \[\frac{1}{2}{{\pi }^{2}}{{a}^{3}}\]
D) \[{{\pi }^{2}}{{a}^{3}}\]
Correct Answer: C
Solution :
Key Idea: Volume\[=2\int_{0}^{\infty }{\pi {{y}^{2}}}dx\] The figure of the given curve \[y=\frac{{{a}^{3}}}{{{a}^{2}}+{{x}^{2}}}\]is \[\therefore \] Required volume \[=2\int_{0}^{\infty }{x\,{{y}^{2}}}dx\] \[=2\pi {{a}^{6}}\int_{0}^{\infty }{\frac{1}{{{({{a}^{2}}+{{x}^{2}})}^{2}}}}dx\] \[=\frac{{{\pi }^{2}}{{a}^{3}}}{2}\]cu unitYou need to login to perform this action.
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