Find the Area of the Surface Over the Given Region

Multiple Choice

Find the area of the surface over the given region. Use a computer algebra system to verify your results. The sphere, $\overrightarrow { \mathbf { r } } ( u , v ) = 10 \sin u \cos v \hat { \mathbf { i } } + 10 \sin u \sin v \hat { \mathbf { j } } + 10 \cos u \hat { \mathbf { k } } , \quad 0 \leq u \leq \pi , 0 \leq v \leq 2 \pi$

A) $100 \pi$
B) $400 \pi$
C) $200 \pi$
D) $800 \pi$
E) $500 \pi$