Question 49

A 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?

Solution

Let say, radius of the circle is r.

Area of the square =484 sq. cm.

So,Side of the square$$\sqrt{484\ }=22$$ cm.

same wire is used to form the circle.

So, perimeter of the circle will be same as perimeter of the square.

So, $$2\times\pi\ \times r=4\times\ 22.$$

or,$$r=\frac{88\ }{2\pi\ }=14.$$

So,Area of the circle$$\pi r^2=\pi\times14^2=\ \frac{\ 22}{7}\times14^2=616\ cm^2.\ $$

B is correct choice.

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