Chapter 11.3, Problem 3CYU

To determine

To calculate: The diameter of a circle with given area $74m{m}^2$ .

Answer to Problem 3CYU

The diameter of the circle is $9.70474936mm$ .

Explanation of Solution

Given information: Area of the given circle is given here $74m{m}^2$ .

Calculation:

So to calculate the diameter of the given circle, need to know two things

1. Diameter −that is the double of the radius of the circle

Means

  $d=2r$

Where d is the diameter of the circle and r is the radius of the given circle.

2. Area of the circle with radius r is given by

  $A=\pi r^2$

Hence now by using the above results, we get

  $A=\pi r^2$

  $\begin{array}{l} 74=\frac{22}{7}.r^2\hfill \\ 74\times 7=22.r^2\hfill \\ 518=22.r^2\hfill \\ r^2=\frac{518}{22}\hfill \\ r^2=\frac{259}{11}\hfill \end{array}$

  $\begin{array}{l} r^2=23.5454545\hfill \\ r=4.85237468mm\hfill \\ sothisistheradiusofthegivencircle.\hfill \\ Nowdiameterofthegivencircle\hfill \\ =2r\hfill \\ =2\times 4.85237468\hfill \\ =9.70474936mm\hfill \end{array}$