Let r be a positive constant. Consider the cylinder , and let C be the part of the cylinder that satisfies
a) Consider the cross section of C by the plane x = t ( ), and express its area in terms of r,t.
b) Calculate the volume of C, and express it in terms of r.
c) Let a be the length of the arc along the base circle of C from the point (r,0,0) to the point (
Let b be the length of the line segment from the point ( to the point . Express a and b in terms of .
d) Calculate the area of the side of C with , and express it in terms of r.