Question
Download Solution PDFA wire when bent in the form of a square encloses an area of 484 sq. cm. If the same wire is bent in the form of a circle, what is the area enclosed by it?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFArea of the square = 484 sq. cm
Let each side b x cm
x2 = 484
⇒ x = √484 = 22 cm
∴ Length of the wire = 4 × 22 = 88 cm
∴ Circumference of the desired circle = 88 cm
⇒ 2 × (22/7) × radius = 88
⇒ radius = 14 cm
∴ Area = πr2 = (22/7) × 14 × 14 = 616 sq. cm
Smart Trick
Here, area of circle is a multiple of π and radius of the circle. Hence, answer must be a multiple of 11 and 7.
In all given options, we find 616 is the only option that is divisible by 7 and 11 both.
∴ Option 2 is the correct answer.
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