Question

The volume of solid 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. $\frac{2}{15}\pi$
• D. $\frac{5}{24}\pi$

Answer 1

Answer: (C)

$V=\underset{0}{\overset{1}{\int }}\pi x^{2}dy$

$=\left|\pi \underset{0}{\overset{1}{\int }}\left(y^4-y\right)dy\right|$
$=\pi {\left[\frac{y^5}{5}-\frac{y^2}{2}\right]}_0^1\mid$
$=\left|\pi \left[\frac{1}{5}-\frac{1}{3}\right]\right|$
$=\left|\frac{-2\pi }{15}\right|=\frac{2\pi }{15}$