Find the area of the surface. The part of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 16$ that lies above the plane $z = 1$ .
A) $24 \pi$
B) $\frac { \pi } { 16 }$
C) $24$
D) $\pi$
E) $24 - \pi$

Question

Quizplus · Accepted Answer

The sphere has a radius of 4, and the plane $z = 1$ intersects the sphere above the center. The surface area of the spherical cap can be calculated using the formula $2\pi rh$, where $r$ is the radius of the sphere and $h$ is the height of the cap. Here, $h = 4 - 1 = 3$, so the area is $2\pi \times 4 \times 3 = 24\pi$.

Find the Area of the Surface x2+y2+z2=16x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 16x2+y2+z2=16

Find the Area of the Surface $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 16$