Could someone check my work please? The question said to write an integral in spherical coordinates and evaluate it to find the mass of the hemisphere: $x^2+y^2+z^2\leq4; z\geq0$ if the density $\rho(x,y,z)$ is equal to $2z$.
My work:
$m= \iiint_Q\rho(x,y,z) dV $
$m$ = $\displaystyle \int_0^\frac{\pi}{2}\int_0^{2\pi}\int_0^22\rho^3\cos\phi\sin\phi \ d\rho \ d\theta \ d\phi = 8\pi$