Please See Attached
You are going to be using the formula
$\displaystyle V=\int^b_aA(x)dx$
First see that you are taking the integral from $\displaystyle x=0$ until $\displaystyle x=8$ that is when it intersects the x and y axes.
Now you need to find $\displaystyle A(x)$:
Notice that $\displaystyle x+2y=8$ implies $\displaystyle y=-\frac{1}{2}x+8$.
At $\displaystyle x$ the width of the line perpendicular to the x-axis is then $\displaystyle -\frac{1}{2}x+8$. But this is the diameter of the circle. Thus, its radius is $\displaystyle -\frac{1}{4}x+4$.
The area of this cross section (semicircle) is
$\displaystyle \pi \frac{1}{2}\left(-\frac{1}{4}x+4\right)^2$ (remember the 1/2 it is semi-circle )
Thus,
$\displaystyle V=\pi \int^8_0\frac{1}{2}\left(-\frac{1}{4}x+4\right)^2dx=\pi \cdot 37.\bar 3\approx 116$
I think there is something wrong with your choices.