$\"\"$

(a)

Height of the cylinder is $\"\"$ and inner radius is $\"\"$ .

Thickness is $\"\"$ .

Volume of the cylinder is $\"\"$ .

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

Substitute $\"\"$ and $\"\"$ in the above expression.

$\"\"$ .

Approximate volume is $\"\"$ .

$\"\"$

(b)

Actual formula for volume is $\"\"$ .

Outside radius of the cylinder is $\"\"$ .

Inner radius of the sphere is $\"\"$ .

$\"\"$

Absolute error is difference between actual volume and approximate volume.

$\"\"$

(a) Approximate volume is $\"\"$ .

(b) $\"\"$ .