Chapter 9.3, Problem 36E

a.

To determine

To solve formula for r .

Answer to Problem 36E

  $r=0.5640\sqrt{A}$

Explanation of Solution

Given information:

The area of circle

  $A=\pi r^2$

Calculation:

The area of circle

  $A=\pi r^2$

Divide both sides by pi

  $\frac{A}{\pi }=r^2$

On solving

  $r=0.5640\sqrt{A}$

b.

To determine

To find radius of each circle.

Answer to Problem 36E

  $r\approx 5.9962ft$

  $r\approx 23.9981in$

  $r\approx 12.9982m$

Explanation of Solution

Given information:

  

Formula used:

  $r=0.5640\sqrt{A}$

Calculation:

Radius of circle

Area $=113f{t}^2$

Using formula

  $r=0.5640\sqrt{113}$

On solving

  $r\approx 5.9962ft$

Radius of circle

Area $=1810i{n}^2$

Using formula

  $r=0.5640\sqrt{1810}$

On solving

  $r\approx 23.9981in$

Radius of circle

Area $=531m^2$

Using formula

  $r=0.5640\sqrt{531}$

On solving

  $r\approx 12.9982m$

c.

To determine

To explain why it is beneficial to solve formula for r before finding the radius.

Answer to Problem 36E

Easy and less time consuming process of radius finding.

Explanation of Solution

Given information:

  $r=0.5640\sqrt{A}$

The area of circle is $A=\pi r^2$

When finding radius of circle substitute value of area and divide by pi .After this square root the result

The radius of circle is $r=0.5640\sqrt{A}$

Firstly square root the area of circle and multiply by factor $0.5640$

It is easy and less time consuming process of radius finding.