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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.