Please See Attached
Hello,Originally Posted by frozenflames
first you have to calculate the radius of the rotation, which is here the x-coordinate of every point of the curve:
$\displaystyle y=\sqrt{x}\ \Longrightarrow \ x=y^2$
in general the volume of a rotating curve is calculated as
$\displaystyle V=\pi \cdot \int{r^2\ dy}$
Then $\displaystyle V=\int^{2}_{0}{\pi \cdot (y^2)^2 dy=\pi \cdot \left[\frac{1}{5} y^5 \right]^{2}_{0}$
So the right answer is A: $\displaystyle \frac{32}{5} \pi$
Greetings
EB