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)

$\frac{2}{15}\pi$

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