원통 좌표계 사용: 0 \le r \le 2,\ 0 \le \theta \le 2\pi,\ 0 \le z \le r\cos\theta + 4.
V = \int_0^{2\pi} \int_0^2 \int_0^{r\cos\theta + 4} r\, dz\, dr\, d\theta
V = \int_0^{2\pi} \int_0^2 r(r\cos\theta + 4)\, dr\, d\theta= \int_0^{2\pi} \left( \int_0^2 (r^2 \cos\theta + 4r)\, dr \right) d\theta
= \int_0^{2\pi} \left[ \dfrac{1}{3} r^3 \cos\theta + 2r^2 \right]_{0}^{2} d\theta= \int_0^{2\pi} \left( \dfrac{8}{3}\cos\theta + 8 \right) d\theta
V = \left[ \dfrac{8}{3}\sin\theta + 8\theta \right]_{0}^{2\pi}= (0 + 16\pi) - (0 + 0)= 16\pi