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Question:

A square garden is to be built inside a circular area. Each corner of the square touches the circle. If the radius of the circle is 2, how much greater is the area of the circle than the square?

A
4π – 8

Explaination

Find the difference between the area of the circle and the area of the square. The area of the circle is πr^{2}= π× 2^{2}= 4π. The area of the square is s^2^{2}, where s represents the length of the square. The radius is half the length of the square’s diagonal, so the diagonal is 4. By the Pythagorean theorem, s^{2}+ s^{2}= 4^{2}. 2s^{2}= 16 so s^{2}= 8. The difference in area is 4π –8.