Calculating Arc Length and Area of Cylinder Side

[help]

Homework Statement

Let r be a positive constant. [/B]
Consider the cylinder x2 + y2 ≤ r2, 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.

Homework Equations

[/B]
Not sure

The Attempt at a Solution

I used the formula[/B]

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[f '(x)]² = x²/(r²-x²)

... r∫^π₀dθ=? the answer ir θr

 

[BvU]

Hello help,

Make a sketch. For $a$ it can even be a simple 2D sketch.