Question

Find the surface area of the part of the sphere x² + y² + z² = 25 that lies above the cone z=√(x² + y²)

Answer 1

To find the surface area, we use double integrals and convert to cylindrical coordinates.

Step-by-step explanation:

To find the surface area of the part of the sphere x² + y² + z² = 25 that lies above the cone z=√(x² + y²), we can use the concept of double integrals.

We can express the surface area as the integral of the function √(1 + (dz/dx)² + (dz/dy)²) over the region of the cone.

To evaluate this integral, we can convert to cylindrical coordinates and integrate with respect to θ, ρ, and z over the appropriate bounds.