Let r be a positive constant. Consider the cylinder $\displaystyle x^2+y^2≤r^2$ and let C be the part of the cylinder that satisfies 0 ≤ z ≤ y.

(3) Let a be the length of the arc along the base circle of C from the point (r, 0, 0) to the point (r cos θ, r sin θ, 0) (0 ≤ θ ≤ π). Let b be the length of the line segment from the point (r cos θ, r sin θ, 0) to the point (r cos θ, r sin θ, r sin θ). Express a and b in terms of r, θ.

( 4) Calculate the area of the side of C with x2+y2 = r2, and express it in terms of r. 2. Relevant equations Not sure 3. The attempt at a solution

I used the formula . [f '(x)]² = x²/(r²-x²) ... r∫π0dθ=??? the answer ir θr