A circle of radius 7 cm is inscribed in a square. Find the area of the shaded region. Use π=22/7.
length of square =2×8
(circle, square, radius, area, pi)
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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 is given as 7 cm, the diameter will be twice the radius.
Step 2: Calculate the area of the square
Now that we have the side length of the square, we can calculate its area using the formula for the area of a square, which is side multiplied by side.
Step 3: Calculate the area of the circle
Next, we calculate the area of the inscribed circle using the formula πr2. We are given the radius r=7 cm and instructed to use π=22/7.
Step 4: Calculate the area of the shaded region
The shaded region is the area of the square that is not covered by the circle. Therefore, we subtract the area of the circle from the area of the square to find the area of the shaded region.