Chapter 12.4, Problem 50STP

To determine

To find:

The ratio between circle and square.

Answer to Problem 50STP

The required ratio is $\frac{\pi }{4}$ .

Explanation of Solution

Given information:

  

Calculation:

The radius of circle is $2x$ .

So, the area of the circle is:

  $\begin{array}{c}{A}_1=\pi r^2\\ =\pi {\left(2x\right)}^2\\ =4\pi x^2\end{array}$

The side of the square is $2$ times the radius of the circle i.e., $s=4x$ .

So, the area of the square is:

  $\begin{array}{c}{A}_2=s^2\\ ={\left(4x\right)}^2\\ =16x^2\end{array}$

Required ratio is as follows:

  $\begin{array}{c}\frac{A_1}{A_2}=\frac{4\pi x^2}{16x^2}\\ =\frac{\pi }{4}\end{array}$

Hence, the required ratio is $\frac{\pi }{4}$ .