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Question:

A cow is tied to a silo with radius r with a rope just long enough to reach the opposite side of the silo.?

Find the area available for grazing by the cow.

Answer:

ITS THE SAME AS long enough to reach the opposite side of the silo.
If the rope allows the cow to reach a spot on the opposite side of the silo, then the rope must be half of the circumference of the silo. If the radius of the silo is r, then the length of the rope is PI * r. The area that the cow can graze is the area of a circle with radius PI * r, or PI * (PI * R) * (PI * R) or PI ** 3 * r ** 2 (PI cubed times r squared) minus the area of the silo which is PI * R ** 2. The grazing area is then PI ** 3 * R ** 2 - PI * R ** 2 (PI cubed times r squared - PI times R squared). You can then factor to simplify the expression. HTH

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