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RS Aggarwal Solutions Class 10 Mathematics Solutions for Area Of Circle Sector And Segment Exercise 16A in Chapter 16 - Area Of Circle Sector And Segment
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A copper wire when bent in the form of a square encloses an area of 484 cm^2. The same wire is not bent in the form of a circle. Find the area enclosed by the circle.
Answer:
Let the square be of side ‘a’ cm and radius of the circle be ‘r’
The area enclosed by the square = 484 cm^2
Also, we know that Area of square = Side × Side
Area of the square = a^2
=> a^2 = 484
=> a = √484
=> a = 22
Therefore, the side of the square is 22 cm.
Perimeter of square = 4 x side = 4 x 22 = 88
From the statement, the circumference of the circle = Perimeter of a square
2πr = 88
r = (88 x 7)/(2x22) = 14
The radius of the circle = 14 cm
Area of circle = πr^2 = 22/7 x 14 x 14 = 616 cm^2.
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