I am having a tough time understanding how to get the cross sectional areas which you integrate:

The base of a solid is the region bounded by $\displaystyle y=x^{2}$ and y=4. Find the volume of the solid given that the cross sections perpendicular to the x-axis are (a)squares; (b)semicircles; (c)equilateral triangles

the answer to (a) shows $\displaystyle \int(4-x^{2})^{2}\$(from -2 to 2) from what I have tried to understand, the reason it's squared is because its a square so you are multiplying 2 equal lengths but I don't understand how $\displaystyle 4-x^{2}$ would be the distance in the bounded region.

Thanks in advance.