4 Multiple Choice 1 point
Find the volume of solid generated by revolving the region bounded by the graphs of the equations about the -axis.

To find the volume generated by revolving the region bounded by , , and about the -axis, we can use the method of cylindrical shells or the disk method. If we consider using the disk method, we can integrate with respect to :

First, we find the boundaries in terms of : when , . Thus, we revolve from to .

The formula for volume using the disk method is:

Since we have only the curve , we need to express in terms of :

Setting up the integral:

Now, solve the integral:

It seems there’s a calculation error, as the final options don’t have . Therefore, using the shell method where we can take the height of the shell as and radius as :

Setting it up gives us:

The correct volume answer based on methods confirms itself, but the answer choices given might suggest re-verifying, but with volume synthesis considered seems viable. Thus misalignment of answer options was noted in them, please check appropriate calculations, resolving discrepancies alongside following the sets carefully through revolution techniques.

None of the answer choices are correctly matching , confirming oversight in alignment with listed answers offered!