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

Printable View

- 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

$\displaystyle \pi r^2$

$\displaystyle =\pi42^2$

$\displaystyle =1764\pi$

Now, the total amount of wire is the circumference of the circle. This is $\displaystyle \pi\times d$ Where d is the diameter of the circle. As the diameter is twice the radius, $\displaystyle d=84$ and the total amount of wire is $\displaystyle 84\pi$

Now then, one side of the square will be

$\displaystyle \displaystyle\frac{84\pi}{4}$

$\displaystyle =21\pi$

The area of the square will be $\displaystyle width \times height$

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