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There is a square with four circles drawn such that the four corners of the square are the centers of the four circles. What is the ratio of the area of the square to the area enclosed between the circumferences of the circles? The radius of the circle is given as 7 units and side of the square is equal to the diameter of the circles.

There is a square with four circles drawn such that the four corners of the square are the centers of the four circles. What is the ratio of the area of the square to the area enclosed between the circumferences of the circles? The radius of the circle is given as 7 units and side of the square is equal to the diameter of the circles. Correct Answer 14 : 3

GIVEN:

The radius of the circle is given as 7 units and the side of the square is equal to the diameter of the circles.

FORMULA USED:

Area of quadrant of circle = (1/4) π r2  (where r is the radius of the circle)

Area of a circle = πr2

CALCULATION:

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The area enclosed between the circumferences of circles = Area of a square enclosed by the centres of the circle - an area of the 4 sectors of circles.

⇒ 142 - 4× (1/4) π (7)2 

⇒ 196 - 154  =42 cm2

Hence, Ratio is of the square to the area enclosed between the circumferences of the circles

⇒ 196 : 42 = 14 ∶ 3

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