# [SOLVED] Integration: Volume of Solids

• Dec 16th 2008, 05:41 PM
sazafraz
[SOLVED] Integration: Volume of Solids
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 $y=x^{2}$ 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 $\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 $4-x^{2}$ would be the distance in the bounded region.

what is the vertical distance between one point on the line $y = 4$ and the point directly below it on the parabola $y = x^2$ ?