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
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?