The curve \(C\) has polar equation

\(r=5\sqrt{\cot\theta},\qquad 0.01\le \theta\le \frac12\pi.\)

(i) Find the area of the finite region bounded by \(C\) and the line \(\theta=0.01\), showing full working. Give your answer correct to 1 decimal place.

Let \(P\) be the point on \(C\) where \(\theta=0.01\).

(ii) Find the distance of \(P\) from the initial line, giving your answer correct to 1 decimal place.

(iii) Find the maximum distance of \(C\) from the initial line.

(iv) Sketch \(C\).