# Calculus

Find the area of the largest rectangle that fits inside a semicircle of radius 10 (one side of the rectangle is along the diameter of the semicircle).

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1. Hmmm. If you imagine the semicircle being made into a circle, this largest rectangle turns into a square of diagonal 2r. Hmmm. But since it is a square, then each side must be equal to diagonal divided by sqrt 2.

each side=2r/sqrt2
area of square= s^2= 4r^2/2=2r^2
area of the rectangle in the semicircle is half this, or r^2, in this case, 100.
area of semicircle = PI/2 * 100=157

percent of area in the semicircle occupied by square: 100/157=.637

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bobpursley

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