Question

Find the volume of the solid of revolution formed by rotating the curve $y=\sqrt[3]{3x}$ along x-axis bounded by lines $x=0$ and $x=1$?

• A. $\frac{3\pi }{2}$
• B. $\frac{2\pi }{3}$
• C. $\frac{3\pi }{5}$
• D. $\frac{5\pi }{3}$

Answer 1

The correct option is C $\frac{3\pi }{5}$

Volume of the disc $=\pi y^{2}dx$

$=\pi {\int }_0^1{x}^{\frac{2}{3}}dx$

$=\pi \frac{{\left[x^{\frac{5}{3}}\right]}_0^1}{\frac{5}{3}}$

$=\frac{3}{5}\pi$