A circle of 6 radius 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 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. Since the side length of the square is 12 cm, its area will be 122=144 cm2.
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 cm2.
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 (36π cm2) from the area of the square (144 cm2). This gives us 144−36π cm2.