A wire bent in the form of a circle of radius 42 cm is cut & again bent in the form of a square. How do I find the ratio of the regions enclosed by the circle & the square in the two cases?

Thanks,

Ron

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- Feb 28th 2011, 07:42 AMrn5aMensuration
A wire bent in the form of a circle of radius 42 cm is cut & again bent in the form of a square. How do I find the ratio of the regions enclosed by the circle & the square in the two cases?

Thanks,

Ron - Feb 28th 2011, 07:51 AMQuacky
I hope I've understood the question correctly! I'm infamous for misinterpreting what they're asking of me.

The area of the circle initially is

Now, the total amount of wire is the circumference of the circle. This is Where d is the diameter of the circle. As the diameter is twice the radius, and the total amount of wire is

Now then, one side of the square will be

The area of the square will be

So what will the area of the square be? And then, can you finish the question?