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# 9.18: Radius or Diameter of a Circle Given Area

Difficulty Level: At Grade Created by: CK-12

### Let’s Think About It

License: CC BY-NC 3.0

Clara took her little sister, Grace, to the fish pond at the local park. Grace saw a penny in the center of the pond and wanted Clara to reach it for her. A sign stated that the area of the pond was 113.04 sq. ft. Can Clara reach the penny without falling in?

In this concept, you will learn how to find the radius (and diameter) of a circle if you know its area.

### Guidance

The formula for the area of a circle, A=πr2\begin{align*}A=\pi r^2\end{align*}, can also be used to solve for the radius and diameter.

Let’s look an example.

The area of a circle is 113.04 square inches. What is its radius?

First, write the formula.

A=πr2

Next, substitute in what you know.

113.04=(3.14)r2

Next, begin isolating the r\begin{align*}r\end{align*} by dividing both sides of the equation by 3.14.

36=r2

Then, take the square root of both sides.

6=r

The answer is r=6\begin{align*}r = 6\end{align*}. The radius of the circle is 6 inches.

### Guided Practice

What is the diameter of a circle if its area is 379.94 cm2\begin{align*}379.94 \ cm^2\end{align*}?

First, write the formula.

A=πr2

Next, substitute in what you know.

379.94=(3.14)r2

Next, begin isolating the r\begin{align*}r\end{align*} by dividing both sides of the equation by 3.14.

121=r2

Then, take the square root of both sides.

11=r

Remember that you are solving for the diameter.

ddd===2r2×1122

The answer is the diameter, d=22 cm\begin{align*}d = 22 \ cm\end{align*}.

### Examples

#### Example 1

Solve for the radius of a circle if area=153.86 sq. in.\begin{align*}\text{area}= 153.86 \ sq. \ in.\end{align*}

First, write the formula.

A=πr2

Next, substitute in what you know.

153.86=(3.14)r2

Next, begin isolating the r\begin{align*}r\end{align*} by dividing both sides of the equation by 3.14.

49=r2

Then, take the square root of both sides.

7=r

The answer is r=7\begin{align*}r = 7\end{align*}. The radius of the circle is 7 inches.

#### Example 2

Find the radius of a circle with an area of 379.94 sq. ft.

First, write the formula.

A=πr2

Next, substitute in what you know.

379.94=(3.14)r2

Then, begin isolating the r\begin{align*}r\end{align*} by dividing both sides of the equation by 3.14.

121=r2

Take the square root of both sides.

11=r

The answer is r=11\begin{align*}r = 11\end{align*}. The radius of the circle is 11 feet.

#### Example 3

The area of a circle is 452.16 sq. m. Find its radius.

First, write the formula.

A=πr2

Next, substitute in what you know.

452.16=(3.14)r2

Then, begin isolating the r\begin{align*}r\end{align*} by dividing both sides of the equation by 3.14.

144=r2

Take the square root of both sides.

12=r

The answer is r=12\begin{align*}r = 12\end{align*}. The radius of the circle is 12 meters.

License: CC BY-NC 3.0

Remember Clara and Grace at the circular 113.04 sq. ft. fish pond?

Clara wondered if she could reach a penny in the middle without falling in.

First, write the formula.

A=πr2

Next, substitute in what you know.

113.04=(3.14)r2

Then, begin isolating the r\begin{align*}r\end{align*} by dividing both sides of the equation by 3.14.

36=r2

Take the square root of both sides.

6=r

The answer is r=6\begin{align*}r = 6\end{align*}. The radius of the circle is 6 feet. Unless Clara wants to swim with the goldfish, she’d best leave the penny where it is!

### Explore More

Find each radius given the area of the circle.

1. 12.56 sq. in.

2. 78.5 sq. m

3. 200.96 sq. cm

4. 254.34 sq. in

5. 7.07 sq. ft.

6. 28.26 sq. m

Find each diameter given the area of the circle.

7. 12.56 sq. in.

8. 78.5 sq. m

9. 200.96 sq. cm

10. 254.34 sq. in

11. 7.07 sq. ft.

12. 28.26 sq. m

13. 615.44 sq. feet

14. 176.625 sq. m

15. 113.04 sq. ft.

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 9.18.

1. [1]^ License: CC BY-NC 3.0
2. [2]^ License: CC BY-NC 3.0

## Date Created:

Dec 02, 2015

Dec 02, 2015
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