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Multivariable Calculus

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Moderate

Spherical Description

MVCALC-TBGLLR

The surface $S$ consists of the portion of the sphere:

$$x^2+y^2+z^2=9$$

...where:

$$y^2+z^2\geq 1$$

A good description of $S$ in spherical coordinates $(\rho, \theta, \varphi)$ is

A

$S=\{(1, \theta, \varphi): 0\leq \theta\leq 2\pi, \quad 0\leq \varphi\leq \pi, \quad \cos^2\varphi\cos^2\theta \leq \cfrac{2}{3}\}$

B

$S=\{(1, \theta, \varphi): 0\leq \theta\leq 2\pi, \quad 0\leq \varphi\leq \pi, \quad \sin^2\varphi\cos^2\theta \leq \cfrac{2}{3}\}$

C

$S=\{(1, \theta, \varphi): 0\leq \theta\leq 2\pi, \quad 0\leq \varphi\leq \pi, \quad \sin^2\varphi\sin^2\theta \leq \cfrac{8}{9}\}$

D

$S=\{(3, \theta, \varphi): 0\leq \theta\leq 2\pi, \quad 0\leq \varphi\leq \pi, \quad \cos^2\varphi\sin^2\theta \leq \cfrac{2}{3}\}$

E

$S=\{(3, \theta, \varphi): 0\leq \theta\leq 2\pi, \quad 0\leq \varphi\leq \pi, \quad \sin^2\varphi\cos^2\theta \leq \cfrac{8}{9}\}$