Question

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line y = 4.

y = x,   y = 3,    x = 0

Answer 1

Step 1:

The equations are and .

The volume of the solid generated revolving about the line .

Washer method:

Formula for volume of solid

Where is outer radius and is inner radius.

The outer radius of revolution is .

The inner radius of revolution is .

Step 2:

Substitute , in .

.

Integrate between 0 and 3.

Apply power rule in integration .

The volume of solid is cubic units.

Solution:

The volume of solid is cubic units.