Question

Find the volume of the solid generated by revolving the region bounded by the curves x=y^2, x=2, y=0; about y=0

Answer 1

We have given the curve,

$x = y^2,x = 2,y = 0$

Volume of solid can be calculated as,

$V = \pi \int_{0}^{2}(\sqrt{x})^2dx$

$V = \pi \int_{0}^{2}xdx$

$V = \pi \times\dfrac{4}{2}$

$V = 2 \pi$