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Question
A wire is bent to form a square enclosing an area of 484 cm2. Using the same wire, a circle is formed. Find the area of the circle.
Solution
Area of the square = 484 cm2
Area of the square = Side2
⇒ 484 = Side2
222 = Side
Perimeter of the square = 4 Side
Perimeter of the square = 4 × 22 = 88 cm
Length of the wire = 88 cm
Circumference of the circle = Length of the wire = 88 cm
Now, let the radius of the circle be r cm.
Thus, we have:
2πr = 88
`=> 2 xx 22/7 xx r = 88`
⇒ r = 14
Area of the circle = πr2
`=> 22/7xx14xx14`
= 616 x m2
Thus, the area enclosed by the circle is 616 cm2.
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