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**provasanteriores** Any tips?

Let r be a positive constant. Consider the cylinder $\displaystyle x^2 + y^2 \leq r^2$, and let C be the part of the cylinder that satisfies

$\displaystyle 0 \leq z \leq y .$

a) Consider the cross section of C by the plane x = t ($\displaystyle -r \leq t \leq r .$), 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 ($\displaystyle rcos \theta, rsin \theta, 0) 0 \leq \theta \leq \pi .$

Let b be the length of the line segment from the point ($\displaystyle rcos \theta, rsin \theta, 0)$ to the point $\displaystyle (rcos \theta, rsin \theta, rsin \theta).$ . Express a and b in terms of $\displaystyle r, \theta.$ .

d) Calculate the area of the side of C with $\displaystyle x^2 + y^2 = r^2$, and express it in terms of r.