A circle of radius 9 cm is inscribed in a square. Find the area of the shaded region. Use π=722.
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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 9 cm, the diameter will be 2×9 cm=18 cm. Therefore, the side length of the square is 18 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 18 cm, the area of the square is 182=324 cm2.
Step 3: Calculate the area of the circle
The area of a circle is calculated using the formula πr2. Given the radius r=9 cm and π=722, the area of the circle is 722×(9 cm)2=722×81 cm2=71782 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, 324 cm2−71782 cm2=7324×7−1782 cm2=72268−1782 cm2=7486 cm2.