Final answer:
To find the volume of a solid obtained by rotating a region bounded by a shape, set up the appropriate integral based on the shape of the region and evaluate it over the appropriate bounds.
Step-by-step explanation:
The volume of the solid obtained by rotating a region bounded by a shape about an axis can be calculated using the method of integration. First, we need to determine the shape of the region bounded by the given boundary. Once the shape is identified, we can set up the integral to find the volume of the solid. The integral will involve squaring the radius of the shape and multiplying it by the appropriate constant factor, depending on the shape. Taking the definite integral over the appropriate bounds will give us the volume of the solid obtained by rotating the region.