A Circle of radius 7 cm is inscribed in a Square. Find area of the shaded region. Use π=22/7.
196−154=42 cm2
(circle, square, radius, area, inscribed)
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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 7 cm, the diameter will be 2×7 cm=14 cm. Therefore, the side length of the square is 14 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 14 cm, the area of the square is 142=196 cm2.
Step 3: Calculate the area of the circle
The area of a circle is calculated using the formula πr2. Given the radius r=7 cm and π=722, the area of the circle is 722×(7 cm)2=722×49 cm2=22×7 cm2=154 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, 196 cm2−154 cm2=42 cm2.