Answer
$\dfrac{\pi}{3} \ cubic \ units $
Work Step by Step
We have the area of an equilateral triangle is: $A(x)=\dfrac{1}{2} \pi r^2=\dfrac{\pi}{8}(2-x)^2$
The volume of a solid can be computed as:
$V=\int_a^b A(x) dx=\int_0^2 \dfrac{\pi}{8}(2-x)^2 \ dy \\=\dfrac{\pi}{8} [\dfrac{(2-x)^3}{(3)(-1)}]_0^2 \\=\dfrac{\pi}{3} \ cubic \ units $
