Answer
$\dfrac{ 4 \pi r^3}{3}$
Work Step by Step
The equation of the circle about the x- axis is: $r^2=x^2+y^2$
We need to use the Washer method as follows:
$V=(2) \int_p^{q} (2 \pi) \cdot (\space radius \space of \space shell) ( height \space of \space Shell) \space dy \\= (2) \times \int_{0}^{r} (y) \cdot (\sqrt {r^2-y^2}) dy \\=[\dfrac{-4 \pi (r^2-y^2)^{3/2}}{3}]_{0}^{r} \\=\dfrac{ 4 \pi r^3}{3}$
