The base of the solid is the region between the $x$-axis and the parabola $y=4-x^2$. The vertical cross sections of the solid perpendicular to the $y$-axis are semicircles. Compute the volume of the solid.
I know the area formula for a semicircle is $\frac{(\pi*r^2)}{2}$, but would you use $r=4 - x^2$ even though the question only says the base is made from this parabola?
On
The formula is c-lower limit and d-upper limit integral of A(y) dy .The limits of integration are wrong since you're integrating with respect to y the limits should be 0 to 4 and the ans is 4pi ---for more explanation look up Volume - Cross Sections Perpendicular to the y-axis on youtube. The radius needs to be in terms of y because the cross sections are perpendicular to the y-axis so you solve for x and get +and-sqrt(4-y) and you subtract the positive square root from the negative square root and divide by 2 because you want radius, not diameter then square it and that's how you get (4-y).
Each semicircle has a radius $x$, so the solid has volume
$$\frac{\pi}{2} \int_0^2 dy \, x^2 = \frac{\pi}{2} \int_0^2 dy \, (4-y) = 3 \pi$$