Question

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

Inside the sphere x² + y² + z2 = 16 and outside the cylinder x² + y² = 9

Answer 1

To find the volume of the solid inside the sphere and outside the cylinder, subtract the volume of the cylinder from the volume of the sphere.

Step-by-step explanation:

To find the volume of the given solid, which is inside the sphere and outside the cylinder, we need to subtract the volume of the cylinder from the volume of the sphere.

The volume of the sphere is given by the formula V = (4/3)πr³, where 'r' is the radius of the sphere.

The volume of the cylinder is given by the formula V = πr²h, where 'r' is the radius of the base and 'h' is the height of the cylinder.

Substitute the given values into the formulas, calculate the volumes, and then subtract the volume of the cylinder from the volume of the sphere to find the volume of the solid.