A circle of radius 6cm is inscribed in a square. Find the area of the shaded region. (π=3.14)
Given information:
radius =6cm r=6 d=2×r
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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. We are given that the radius of the circle is 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 π times the radius squared. We are given the radius as 6 cm and π as 3.14.
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 have already calculated both these areas.
Step 5: Final Answer
Subtracting the area of the circle from the area of the square gives us the area of the shaded region.