The arc equation is  on interval .

The arc is revolved about the line .

(a) Find the volume of the resulting solid as a function of .

The volume of the solid generated revolving about the line .

Washer method:

.

Here outer radius .

.

(b)

Graph the function  and label the minimum point.

Graph:

Observe the graph:

The minimum volume is  for .

(c)

Volume of the solid is .

Apply derivative on each side with respect to .

Find the minimum or maximum value by equating .

Apply derivative on each side with respect to .

, the function  has relative minimum.

Therefore, the minimum volume at .

(a) .

(b) Graph of the function :

.

(c) .