Goat tethered to a circular silo

A goat is tethered with a rope of length L to a circular silo of radius r. What area is the goat able to eat?

We examine part of the area. Try various parameters r and L and see if you can conjecture the formula for area in terms of L and r.

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L (length of rope)
r (radius of silo)
tether position
0.00100 0 0.99900
Area of grass

This is only one piece of the total area reachable by the goat. What is the total area?

What happens if the area intersects itself (say r=1, L=10)?

Does the area computation still actually give the correct answer? If not, why not? And if not, how would you compute the correct answer?

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