Length of a spiral in polar coordinates

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Part of my assignment is to find out how to calculate the length of the spiral in the picture in polar coordinates( from point a to b) I wonder if someone can help me. We haven’t really done anything like that in the subject before.

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HINTS:

Coil diameter $2R$, pitch or one turn height $p$.

Length of each turn $= \sqrt{(2\pi R)^2+h^2}$ by screw/helix flattened development and Pythagoras thm which is to be multiplied by

$$ n=\frac{\text{Coil height = H}}{h} $$

Can you sketch the development?