원통 좌표계 사용: 0 \le \theta \le 2\pi, z = r (원뿔), r \le z \le 4, 0 \le r \le 4.

M = \displaystyle\iiint_E z\, dV = \int_0^{2\pi} \int_0^4 \int_r^4 z\, r\, dz\, dr\, d\theta

M = \displaystyle\int_0^{2\pi} d\theta \cdot \int_0^4 r \left[ \dfrac{1}{2} z^2 \right]_{z=r}^{z=4} dr

M = \displaystyle\int_0^{2\pi} d\theta \cdot \int_0^4 r \left( \dfrac{16}{2} - \dfrac{r^2}{2} \right) dr= \int_0^{2\pi} d\theta \cdot \int_0^4\left( 16r - r^3 \right) dr

M = 2\pi \left[ \dfrac{16r^2}{2} - \dfrac{r^4}{4} \right]_0^4= \pi \left( 8(16) - \dfrac{1}{4}(256) \right)= \pi (128 - 64)= 64\pi