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A circle of radius 6 cm is inscribed in a square. Find the area of the shaded region.
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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 6 cm, the diameter is 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. With a side length of 12 cm, 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 is 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 of the square minus the area of the inscribed circle. So, we subtract the area of the circle from the area of the square: 144−36π square cm.