Dividing a circle's circumference by pi (π) results in the circle's diameter.
Understanding the Relationship
The relationship between a circle's circumference (C), diameter (d), and pi (π) is fundamental in geometry. The formula that defines this relationship is:
C = πd
From this formula, we can derive that:
d = C / π
This shows that dividing the circumference by pi gives you the diameter.
Steps to Divide Circumference by Pi
Here's a step-by-step guide:
- Measure or know the circumference (C) of the circle. This is the distance around the circle.
- Divide the circumference (C) by pi (π). Pi is approximately equal to 3.14159. So, diameter (d) = C / π.
Example
If a circle has a circumference of 31.4159 units:
Diameter (d) = 31.4159 / 3.14159 = 10 units
Therefore, the diameter of the circle is 10 units.
Finding the Radius
Once you have the diameter, finding the radius is simple:
- The radius (r) is half of the diameter (d).
- r = d / 2
In our example:
Radius (r) = 10 / 2 = 5 units
Utilizing the Diameter
The reference video extract states the importance of identifying the diameter of a circle. Knowing the diameter (or deriving it from the circumference) is crucial for various calculations related to circles, such as finding the area. In some cases, the radius may be given, and you can calculate the diameter using the formula d = 2r, as also mentioned in the video description.
