Chapter 12.2, Problem 37STP

a)

To determine

To find : An algebraic equation in terms of 'A', that could be sued to find radius of circle.

Answer to Problem 37STP

  $r=\sqrt{\frac{\pi }{A}}$

Explanation of Solution

Given Information :

The given information is, Area of circle is $327.6$ sq.cm.

Formula Used:

  $A=\pi r^2$ , where ' $r$ ' is radius of circle

Calculation :

  $\begin{array}{l}A=\pi r^2\\ \Rightarrow r^2=\frac{A}{\pi }\end{array}$

  $\Rightarrow r=\pm \sqrt{\frac{A}{\pi }}$ , radius can not be negative.

So, ignoring negative value.

  $\Rightarrow r=\sqrt{\frac{A}{\pi }}$

b)

To determine

To find : Radius to the nearest then.

Answer to Problem 37STP

Radius to nearest tenth is $10.2$ cm.

Explanation of Solution

Given Information :

The given information is, Area of circle is $327.6$ sq.cm.

Formula Used:

  $r=\sqrt{\frac{A}{\pi }}$ , from part (a).

Calculation :

  $\begin{array}{l}r=\sqrt{\frac{A}{\pi }}\\ \Rightarrow r=\sqrt{\frac{327.6}{\pi }}=\sqrt{104.278}=10.21\text{cm}\end{array}$

Nearest tenth to $10.21$ cm is $10.2$ cm.