The Lesson
The
radius of a
circle is found from the
circumference of a circle using the formula:
In this formula,
C is the circumference of the circle. The image below shows what we mean by finding the radius from the circumference:
How to Find the Radius from the Circumference
Finding the radius from the circumference is easy.
What is the radius of the circle, with circumference 50 cm, below?
Step-by-Step:
1
Start with the formula:
Radius = C⁄2π
Don't forget: / means ÷
and π is
pi (≈ 3.14)
2
Substitute the circumference into the formula. In our example, C = 50.
Radius = 50⁄2π
Radius = 50 ÷ 2 ÷ π
Radius = 25 ÷ π
Radius = 25 ÷ 3.14
Radius = 8 cm
Answer:
The radius of the circle is 8 cm.
Lesson Slides
The slider below shows another real example of how to find the radius of a circle from the circumference.
Interactive Widget
Here is an
interactive widget to help you learn about finding the radius of a circle from its circumference.
Why Is Knowing the Radius in Terms of the Circumference Useful?
Most of the properties of a circle - such as its
circumference and
area - can be expressed in terms of the radius or diameter.
Most students remember the cirumference of a circle with a diameter
d as:
But what if you are told the radius
r instead? Multiply it by 2 to find the diameter.
If you substitute
2r for
d, a formula for the circumference of a circle in terms of the radius can be found:
how to find the circumference of a circle using the radius