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) $500 \pi$

Question

Quizplus · Accepted Answer

The area of the surface of a sphere with radius $r$ is given by the formula $4\pi r^2$. Given the parameterization of the sphere, the radius $r$ is $10$. Therefore, the surface area is $4\pi (10)^2 = 400\pi$.

Find the Area of the Surface Over the Given Region