Math, asked by kalpnajha1986kp, 1 month ago

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Answered by RvChaudharY50
1

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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Answered by amitnrw
1

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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