Question

Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.

Answer 1

Use polar coordinates to find the volume of the given solid:

Inside the sphere x2+y2+z2=16 and outside the cylinder x2+y2=4.

Answer and Explana

Answer 2

Find the volume of the given solid:

Explanation:

• The integrand is usually of the form z_upper − z_lower, where each z defines the lower and upper boundaries of the solid.
• As it is currently set up, you are treating the sphere as a hemisphere, where your lower boundary is the xy-plane. Hence, you need to multiply by 2.
• Volume of the solid is (√16 - r²) -(-√16 - r²).