Find the surface area of the part of the sphere x² + y²+ z² = 36 between the planes z = 1 and z = 5. A) 12$\pi$ square units B) 288$\pi$ square units C) 48$\pi$ square units D) 96$\pi$ square units E) 144$\pi$ square units

Question

Quizplus · Accepted Answer

The equation of the sphere is $x^2 + y^2 + z^2 = 36$, which represents a sphere centered at the origin with a radius of 6. The surface area of a spherical cap is given by $2\pi Rh$, where $R$ is the radius of the sphere and $h$ is the height of the cap. The height of the cap between $z = 1$ and $z = 5$ is $5 - 1 = 4$. Therefore, the surface area of the part of the sphere between these planes is $2\pi \times 6 \times 4 = 48\pi$ square units.

Find the Surface Area of the Part of the Sphere π\piπ

Find the Surface Area of the Part of the Sphere $\pi$