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Answers
Solution :-
→ Side of square = 14 cm
So,
→ Area of square = (side)² = (14)² = 196 cm²
Now,
→ Side of square = Diameter of one circle + Diameter of second circle .
Let radius of each circle is r cm .
→ 14 = 2r + 2r
→ 4r = 14
→ r = (7/2)
So,
→ Area of all four circles = 4[πr²] = 4 * (22/7) * (7/2)² = 4 * (22/7) * (49/4) = (22/7) * 49 = 22 * 7 = 154 cm² .
therefore,
→ Area of the part of the square enclosed by the circles = Area of square - Area of four circles = 196 - 154 = 42 cm² (Ans.)
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Given : Four circles are described about 4 corners o f a square so that it each touches two of the others.
Side of the square is 14 cm
To Find : Area of the part of the square enclosed by circle
Area enclosed between circumference of the circle ,
Solution:
Radius of the circle = 14/2 = 7 cm
Square has right angles.
Area of sector of one circle inside square = ( 90/360) π(7)²
= (1/4) (22/7) * 7²
= 154/4 cm²
There are total 4 circles
Hence Area of the part of the square enclosed by circles = 4 * 154/4 cm²
= 154 cm²
Area of square = 14² = 196 cm²
Area enclosed between circumference of the circle = 196 - 154 = 42 cm²
If question to be solved as per given figure where circles are inscribed in square
Radius of circle = (7/2) cm
Area of 4 circle = 4 * (22/7) (7/2)² = 154 cm²
Area of the part of the square enclosed by circles = 154 cm²
Area of the square not enclosed by circles = 196 - 154 = 42 cm²
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