Radius or Diameter of a Circle
Given Area
Jen Kershaw
Sue Boskat Murray
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Printed: June 5, 2016
AUTHORS
Jen Kershaw
Sue Boskat Murray
www.ck12.org
C HAPTER
Chapter 1. Radius or Diameter of a Circle Given Area
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Radius or Diameter of a
Circle Given Area
In this concept, you will learn how to find the radius (and diameter) of a circle if you know its area.
Let’s Think About It
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 , 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.
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113.04 = (3.14)r2
Next, begin isolating the r 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. The radius of the circle is 6 inches.
Guided Practice
What is the diameter of a circle if its area is 379.94 cm2 ?
First, write the formula.
A = πr2
Next, substitute in what you know.
379.94 = (3.14)r2
Next, begin isolating the r 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.
d = 2r
d = 2 × 11
d = 22
The answer is the diameter, d = 22 cm.
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Chapter 1. Radius or Diameter of a Circle Given Area
Examples
Example 1
Solve for the radius of a circle if area = 153.86 sq. in.
First, write the formula.
A = πr2
Next, substitute in what you know.
153.86 = (3.14)r2
Next, begin isolating the r 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. 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 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. The radius of the circle is 11 feet.
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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 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. The radius of the circle is 12 meters.
Follow Up
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.
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Chapter 1. Radius or Diameter of a Circle Given Area
First, write the formula.
A = πr2
Next, substitute in what you know.
113.04 = (3.14)r2
Then, begin isolating the r 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. 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!
Video Review
https://www.youtube.com/watch?v=VmXg6Gg69u8
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/169065
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.
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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.
References
1. Peter. https://www.flickr.com/photos/80340800@N05/9102373785 .
2. Kamillo Kluth. https://www.flickr.com/photos/27330306@N08/3758819854 .
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