Question

Find the value of a if the volumeof the solid of revolution formed by rotating the curve $y=\sqrt[9]{9x^2}$ along x-axis bounded by lines $x=0$ and $x=1$ is $\frac{a\pi }{13}$ .

Answer 1

$y=x^{2/9}$ , $x=0$ , $x=1$

$\Rightarrow$ ${\int }_0^1\pi y^{2}dx$

$=\pi {\int }_0^1{x}^{4/9}dx$

$=\pi \frac{x^{13/9}}{\frac{13}{9}}$

$=\frac{9\pi }{13}$

$=2.2$