# 9.18: Radius or Diameter of a Circle Given Area

**At Grade**Created by: CK-12

**Practice**Radius or Diameter of a Circle Given Area

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.

### Finding the Radius or Diameter of a Circle Given Area

The formula for the area of a circle,

Let’s look an example.

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

First, write the formula.

Next, substitute in what you know.

Next, begin isolating the

Then, take the square root of both sides.

The answer is

### Examples

#### Example 1

Earlier, you were given a problem about Clara and Grace, who were 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.

Next, substitute in what you know.

Then, begin isolating the

Take the square root of both sides.

The answer is

#### Example 2

What is the diameter of a circle if its area is

First, write the formula.

Next, substitute in what you know.

Next, begin isolating the

Then, take the square root of both sides.

Remember that you are solving for the diameter.

The answer is the diameter,

#### Example 3

Solve for the radius of a circle if

First, write the formula.

Next, substitute in what you know.

Next, begin isolating the

Then, take the square root of both sides.

The answer is

#### Example 4

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

First, write the formula.

Next, substitute in what you know.

Then, begin isolating the

Take the square root of both sides.

The answer is

#### Example 5

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

First, write the formula.

Next, substitute in what you know.

Then, begin isolating the

Take the square root of both sides.

The answer is

### Review

Find each radius given the area of the circle.

- 12.56 sq. in.
- 78.5 sq. m
- 200.96 sq. cm
- 254.34 sq. in.
- 7.07 sq. ft.
- 28.26 sq. m

Find each diameter given the area of the circle.

- 12.56 sq. in.
- 78.5 sq. m
- 200.96 sq. cm
- 254.34 sq. in.
- 7.07 sq. ft.
- 28.26 sq. m
- 615.44 sq. ft.
- 176.625 sq. m
- 113.04 sq. ft.

### Review (Answers)

To see the Review answers, open this PDF file and look for section 9.18.

### Resources

### Notes/Highlights Having trouble? Report an issue.

Color | Highlighted Text | Notes | |
---|---|---|---|

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Term | Definition |
---|---|

Area |
Area is the space within the perimeter of a two-dimensional figure. |

Circle |
A circle is the set of all points at a specific distance from a given point in two dimensions. |

Diameter |
Diameter is the measure of the distance across the center of a circle. The diameter is equal to twice the measure of the radius. |

### Image Attributions

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

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