Geometry

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Perimeter of a Circle

How to Find the Perimeter of a Circle

The perimeter of a circle is called the circumference. The formula for perimeter of a circle is the circumference formula. It is given as:
C = 2πr
or:
C = πd
Where C is the circumference, r is the radius of the circle, and d is the diameter of the circle. Here is an example of using this formula to find circumference of a circle with a radius of 3.
C = 2π(3) = 6π, circumference = 6π.

dimensions of a circle
    A circle with labeled dimensions.

Example Problems:

Problem 1:
Find the circumference of a circle with a radius of 10.

Solution:
Let’s plug the radius into the circumference formula.
C = 2πr = 2π(10) = 20π
The circumference is 20π.

Problem 2:
Find the circumference of a circle with a diameter of 10.

Solution:
Let’s plug the diameter into the circumference formula.
C = πd = π(10) = 10π
The perimeter is 10π.

Problem 3:
Compare the perimeter of a circle with a diameter of 7 to a square with a side length of 7. The formula for perimeter of a square is P = 4s.

Solution:
Let’s plug the circle’s diameter into the circumference formula. Solving for circumference gives us the perimeter.
C = πd = π(7) = 7π.
Now let’s do the same for the square.
C = 4s = 4(7) = 28
The circle’s perimeter is 7π (≈22) and the square’s perimeter is 28.

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