Originally Posted by

**arbolis** I'm unsure of the way to approach the problem : Let $\displaystyle C:[0,\pi]\to \mathbb{R}^3$ be the curve given by $\displaystyle C(t)=(0,\sin t , t)$. Calculate the volume enclosed by the curve if we rotate $\displaystyle C$ with respect to the $\displaystyle z$ axis.

I think a way would be to determine the solid and then evaluate the volume via a triple/double or even simple integral.

I wonder if there's an easier way to solve the problem.

Otherwise I'm not sure what solid the rotated curve represent. An ellipsoid?