A rectangle 6 feet wide has a circle with a diameter of 6 feet inscribed within. How high is the rectangle if the areas within the circle and outside the circle are equal?

Explanation

If the area of the circle is equal to the area outside the circle, then the area of the rectangle is twice the area of the circle. The circle, with radius r = 3, has an area \(A=\pi \times 3^{2}=9 \pi \approx 28.26\) square feet; twice that is 56.52. Dividing this by 6, the width, gives the result. We choose D here.

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