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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 the 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 the 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 the square = (Side)2

Area of a circle = πr2

CALCULATION:

Side of the square = Diameter of circle = 2 × radius = 2 × 7 = 14 units

Area of the square = 142 = 196 sq. units

The area enclosed between the circumferences of the circles

⇒ Area of the square – (4 × 1/4 × π × 72)

⇒ 196 – 154

⇒ 42

Hence,

Ratio area of the square to the area enclosed between the circumferences of the circles = 196 : 42 = 14 ∶ 3

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