원판법을 사용한다.

V = \pi \displaystyle \int_{0}^{\frac{\pi}{2}} y^2 dx = \pi \displaystyle \int_{0}^{\frac{\pi}{2}} \sin^2 x dx

\sin^2 x = \dfrac{1 - \cos(2x)}{2}를 사용한다.

V = \pi \displaystyle \left[\dfrac{1}{2}x - \dfrac{1}{4}\sin(2x)\right]_{0}^{\frac{\pi}{2}} = \pi \left[\left(\dfrac{\pi}{4} - \dfrac{1}{4}\sin(\pi)\right)-(0)\right]

V = \pi \left(\dfrac{\pi}{4} - 0\right) = \dfrac{\pi^2}{4}