Q. The volume of the solid is generated by revolving about the $y$-axis. The figure bounded by the parabola $y = x^{2}\ and\ x = y^{2}$ is
A) $\frac{21}{5}\pi$
B) $\frac{24}{5}\pi$
C) $\frac{3\pi}{10}$
D) $\frac{5}{24}\pi$
Explanation
(c)
$\therefore Required\ volume$
$V = \left| \int_{0}^{1}{\pi\ x^{2}\ \ dy} \right|$
$= \left| \pi\int_{0}^{1}{(\ y^{4} - \ y})dy \right|$
$= \left| \pi\left\lbrack \frac{y^{5}}{5} - \frac{y^{2}}{2} \right\rbrack_{0}^{1} \right|$
$= \left| \pi\left\lbrack \frac{1}{5} - \frac{1}{2} \right\rbrack \right| = \frac{3\pi}{10}$
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Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.