Problem

二、多選題

14. Let $S$ denote the solid enclosed by $x^2+y^2+z^2=2z$ and $z^2=x^2+y^2$.

(A) The length of of the curve determined by $\{(x,y,z):x^2+y^2+z^2=2z \text{ and } z^2=x^2+y^2\}$ is $2\pi$.

(B) The volume of $S$ is less than less than $2\pi/3$.

(C) The volume of $S$ is equal to $\pi$.

(D) 當使用球面坐標係 $(r,\theta,\phi)$，即 $x=r\sin\theta\cos\phi,\ y=r\sin\theta\sin\phi,\ z=r\cos\theta$ 時，$S$ 的體積等於

$$\int_0^{2\pi}\int_0^{\pi/4}\int_0^{2\cos\phi}\rho^2\sin(\phi)\,\mathrm{d}\rho\mathrm{d}\theta\mathrm{d}\phi。$$

(E) $S$ 的表面積大於 $4\pi$。