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a swimming pool is formed by the intersection of two circles whose radii are both 9m. find the area of the swimming pool formed?

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“A swimming pool is formed by the intersection of two circles whose radii are both 9m. Find the area of the swimming pool formed.”

“Intersection” in this problem must mean the area enclosed by both circles, which will be two circular segments. See http://mathworld.wolfram.com/CircularSegment.html.

Missing from the description of this problem is the requisite distance between the centers of the circles.

Here’s an animated gif showing numeric solutions for all relevant distances between the centers of the circles: http://www.wyzant.com/resources/files/265739/intersecting_circles.
The circles must be tangent to each other (just touching at 1 point).  The area will be the sum of the area of each circle.
A = πr² = π(9)² = 81π for each of the two circles.  For the 2 circles combined, A = 2πr² = (2)(81π) = 162π

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