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A circular garden with a radius of 4 ft is planted in the center of a 10 ft square. The part of the square that is NOT the garden is covered with small white rocks. what is the area of the region covered with white rocks?

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First, draw a diagram to visualize the situation:

The area of the region covered with small rocks can be found by subtracting the area of the circle from the area of the square.

The area A_s of a square with side L is given by:


A_s=L^2

And the area A_c of a circle with radius r is given by:


A_c=\pi r^2

Replace r=4ft and L=10ft into the equations to find the area of the circle and the square:


\begin{gathered} A_s=(10ft)^2=100ft^2 \\ A_c=\pi(4ft)^2=16\pi ft^2\approx50.265ft^2 \end{gathered}

Finally, subtract the area of the circle from the area of the square to find the area of the region covered with rocks:


A=A_s-A_c=100ft^2-16\pi ft^2\approx49.7ft^2

Therefore, the area of the region covered with rocks is exactly 100-16π square feet, which is approximately equal to 49.7 square feet.

A circular garden with a radius of 4 ft is planted in the center of a 10 ft square-example-1
User Pyrocrasty
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