$\"\"$

A manfacturer drills a hole through the center of a metal sphere of radius $\"\"$ .

The radius of the hole is $\"\"$ .

$\"\"$

When we rotate a thin horizantal strip as shown in the figure about the $\"\"$ axis, we get a

resulting ring with inner radius $\"\"$ and outer radius $\"\"$ .

The width of the resulting ring is $\"\"$ .

Volume of the resulting ring is $\"\"$ .

$\"\"$

Find volume integrate $\"\"$ to $\"\"$ .

$\"\"$

The volume of the resulting ring is $\"\"$ .