Date: / /
A circle of radius 6 cm is inscribed in a square. Find the area of the shaded region.
The figure shows a square with a circle inscribed within it. The side length of the square is indicated as 6 cm. The region outside the inscribed circle but inside the square is shaded.
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Step-by-Step Solution
Step 1: Determine the side length of the square
When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square. Since the radius of the circle is given as 6 cm, the diameter will be 2×6=12 cm. Therefore, the side length of the square is 12 cm.
Step 2: Calculate the area of the square
The area of a square is calculated by squaring its side length. We found the side length of the square to be 12 cm. So, the area of the square is 122=144 square cm.
Step 3: Calculate the area of the circle
The area of a circle is calculated using the formula πr2, where r is the radius. Given the radius r=6 cm, the area of the circle is π(6)2=36π square cm.
Step 4: Calculate the area of the shaded region
The shaded region is the area inside the square but outside the circle. To find this area, we subtract the area of the circle from the area of the square. So, the area of the shaded region is 144−36π square cm.