A circle of radius 6 cm is inscribed in a square. Find the area of the shaded region. (π=722)
radius = 6 cm
d=2×r =12 cm
Area of Square =d2 =122 =144 cm 2
Area of circle =πr2 =722×6×6 =7792
Area of shaded region
=7144×7−792 =71008−792 =7216
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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. Given the radius of the circle is 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. We calculate 144−7792 by finding a common denominator, which gives 71008−792=7216 cm2.