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 d=2×6=12 cm
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Step-by-Step Solution
Step 1: Determine the side 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. We are given the radius of the circle as 6 cm.
Step 2: Calculate the area of the square
Now that we know the side length of the square is 12 cm, 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 need to find the area of the inscribed circle. The formula for the area of a circle is πr2, where r is the radius. We are given r=6 cm and π=722.
Step 4: Calculate the area of the shaded region
The shaded region is the area of the square minus the area of the circle. We subtract the area of the circle from the area of the square to find the remaining area.
Step 5: Simplify the result
To get the final answer, we perform the subtraction and simplify the fraction.