Hello, I'm back again. I have three problems (two with two parts) that, if you guys wouldn't mind, I would like to have checked. If anything is wrong, I would highly appreciate it if you showed me where I went wrong and how to do it correctly. Thanks infinitely in advance.

Problem 1. Let R be the region bounded by the semicircle y =

and the x-axis.

**a.** Derive the formula for the volume of a sphere of radius r by revolving R about the x-axis using the disk method or the shell method.

My Solution (Using Disk Method)
V =

dx =

=