A circle of radius 6 cm is inscribed in a square. Find the area of the shaded region. (π=722).
radius =6 cm
r=6, 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 =144−7792=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. We are given the radius of the circle, r=6 cm. So, we can find the diameter by multiplying the radius by 2.
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
With the given radius r=6 cm and π=722, we can calculate the area of the circle using the formula Area=πr2.
Step 4: Calculate the area of the shaded region
The shaded region is the area of the square minus the area of the inscribed circle. We subtract the area of the circle from the area of the square to find the remaining area.