A square is inscribed in a circle. If the area of the shaded region is $224 c m 2$ , calculate the radius.

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13cm

12 cm

15 cm

14 cm

answer is D.

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Detailed Solution

It is given that the area of the shaded region is

A = 224 c m 2

We need to calculate the radius.
We know that the area of the shaded region = Area of the circle – Area of the square.
So first we need to find the area of the circle and the square.
Then draw the diagonal of the squares.
By observing the above figure, we can say that the diagonal of a square is the diameter of a circle.
So diagonal of square = diameter of circle.
Let the radius of the circle be r.
Then the diagonal of the square is 2r.
Now let the side of the square be a. We know that the sides of a square are equal. And we know that the diagonal of a square divides the square into an isosceles right triangle. Therefore, we can use the Pythagorean theorem to write,