# Math Help - Mensuration

1. ## Mensuration

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

2. 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
$\pi r^2$

$=\pi42^2$

$=1764\pi$

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

Now then, one side of the square will be
$\displaystyle\frac{84\pi}{4}$
$=21\pi$

The area of the square will be $width \times height$
So what will the area of the square be? And then, can you finish the question?