A circle of radius 6 cm is inscribed in a square. Find the area of the shaded region. Use pi= 22/7
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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 cm=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 cm2.
Step 3: Calculate the area of the circle
The area of a circle is calculated using the formula πr2. Given the radius r=6 cm and π=722, the area of the circle is 722×(6 cm)2=722×36 cm2=7792 cm2.
Step 4: Calculate the area of the shaded region
The shaded region represents the area of the square that is not covered by the circle. To find this area, we subtract the area of the circle from the area of the square. So, 144 cm2−7792 cm2=71008−792 cm2=7216 cm2.