1. ## Area and Volume

The base of a solid is a circle with radius 6. The cross sections of the solid perpendicular to a fixed diameter of the base are squares.

If the circle is centered at the origin and the cross sections are perpendicular to the x-axis, find the area A(x) of the cross section at x and find the volume V of the solid.

2. Well if the cross sections are squares then the length of each side is equal to line drawn across the circle.

For example, at x=0, the bottom line of the area goes through the middle of the circle, so the
area of the cross section is equal to $2(r+r)=4r=4\cdot6$

Can you visualize the shape ?

Can you now find the term for a general x?
Use the fact that this object is highly symmetrical.

Hope that helps.

3. So are you saying that I would need to use y= sqrt((r^2)-(x^2)) with r = 6?

And then, would I have to multiply by 2 for the other side of the circle and finally square the entire thing to find the area equation?

4. Yes that is excatly what I am saying.