I am having trouble understanding a question to a volume problem. The base of a solid S is a circle of radius two in the xy plane centered at the origin. Cross-sections of the solid perpendicular to the base are squares. I am thinking y = 4-X^2. Where do I find the shape for the squares? Can someone explain?
The shape for the squares? Squares are squares! I assume you mean the size of the squares. To answer the title of you post, actually, saying "cross sections of the solid perpendicular to the base" is ambguous. The base is a circle of radius 2 centered at the origin (so x^{2}+ y^{2} or y= +/-√(4- x^{2}) (which is NOT quite what you have) . Imagine you have this object actually sitting in front of you. Take a sharp knife and slice through it. What you the cut side looks like (the cross section), depends on the angle the knife makes with the x and y axes as well as being perpendicular to the xy-plane. I'm going to assume that cross-sections perpendicular to the x-axis are squares. (You hold your knife at right angles to the x-axis as you cut through the figure. The "cut end" looks like a square). A line through the figure, perpendicular to the x-axis runs from -√(4- x^{2}) to +√(4- s^{2}), a total length of 2&radic(4- x^{2}). Being a square, the other sides are the same length and the area of the square is (2√(4-x^{2}))^{2}= 4(4-x^{2}).