# Calculus/Volume of solids of revolution/Solutions

The region extends in the -direction from to . The volume of the solid of revolution is given by

The region extends in the -direction from to . The volume of the solid of revolution is given by

The values of the region extend from to . The volume is

You could set up the appropriate region in any of the four quadrants. Here we set it up in the first quadrant. Since we are revolving around the -axis, the direction will be the height and the radius will be along the direction. So we need a line that passes through the points and . The slope of this line is

and the -intercept is . Thus, the equation of the line is

The -values of the region run from to . Since the function is positive throughout the region we can drop the absolute value sign. The volume will be