Find the volume of a sphere $x^2+y^2+z^2\leq 1$ contained between planes $z=1/2$ and $z=1/\sqrt2$ using cylindrical coordinates.
So the limits of $\theta$ would be $0$ to $2\pi$. Limits of $z$ would be the given planes. But why cant the limits of $r$ simply be $0$ to $1$? Is it because, if this were the case, we would be finding the volume of a cylinder and not a spherical type of object?