Question

The parabolic arc $y=\sqrt{x},1\le \times \le 2$ is resloved around the $x-$axis. The volume of the solid of revolution is

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{2}$
• C. $\frac{3\pi }{4}$
• D. $\frac{3\pi }{2}$

Answer 1

The correct option is D $\frac{3\pi }{2}$

Volume of the elemental dis of thickness $dx$
$dV=\pi y^{2}dx$



$\therefore$ Total volume, $V=\int dV$
$={\int }_1^2\pi y^{2}dx={\int }_{x=1}^2\pi xdx$
$=\frac{\pi }{2}(4-1)=\frac{3\pi }{2}$