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Circumference of a circle




 

In these lessons, we will learn

  • how pi (π) is calculated
  • the formula for the circumference of a circle
  • how to find the circumference of a circle given
    • the diameter of the circle
    • the radius of the circle
  • when given the circumference of a circle, how to find the
    • the diameter of the circle
    • the radius of the circle
    • the area of the circle

  • Circumference of a Circle

    A circle is a closed curve formed by a set of points on a plane that are the same distance from its center. The circumference of a circle is the distance around the circle. It is sometimes called the perimeter of a circle.

    Formula for the Circumference of a Circle

    Calculating the circumference of a circle involves a constant called pi with the symbol π. Pi (π) is the ratio of the circumference of a circle to its diameter. Pi is always the same number for any circle.

    The value of π (pi) is approximately 3.14159265358979323846... but usually rounding to 3.142 should be sufficient. (see a mnemonic for π)

    The formula for the circumference of a circle is

    C = πd     (see a mnemonic for this formula)

    or

    C = 2πr

    where C is the circumference, d is the diameter and r is the radius.

    The diameter of a circle is a line segment that passes through the center of the circle and has its endpoints on the circle. The radius of the circle is a line segment from the center of the circle to a point on the circle. The diameter of a circle is twice the length of its radius.

    If you are given the diameter then use the formula C = πd

    If you are given the radius then use the formula C = 2πr


    The following video shows a fun way to remember the formulas for the circumference of a circle and the area of a circle.
    The following video shows how pi can be calculated for any circle.



    Find the Circumference of a Circle

    The formula for the circumference of a circle is the product of pi (π) and the diameter or twice the product of pi (π) and the radius.

    Example:

    Find the circumference of the circle with a diameter of 8 inches.

    Solution:

    Step 1: Write down the formula: C = πd
    Step 2: Plug in the value: C = 8π

    Answer: The circumference of the circle is 8π ≈ 25.163 inches.

    Example:

    Find the circumference of the circle with a radius of 5 inches.

    Solution:

    Step 1: Write down the formula: C = 2πr
    Step 2: Plug in the value: C = 10π

    Answer: The circumference of the circle is 10 π ≈ 31.42 inches.

    Worksheet to calculate circumference of circle when given diameter or radius. Worksheet to calculate circumference and area of circle when given diameter or radius.
    The following video shows how to find the circumference of a circle given the radius.
    The following video shows examples of how to find the circumference of a circle given the radius or the diameter.


     

    Find the Radius, given the Circumference

    From the formula C = 2πr, we see that we can find the radius of a circle by dividing its circumference by 2π.

    The following video shows how to find the radius of a circle given its circumference.
    Step 1: Find the circumference and substitute.
    Step 2: Divide by π
    Step 3: Divide by 2
    Step 4: Write the units

    Find the Diameter, given the Circumference

    From the formula C = πd, we see that we can find the diameter of a circle by dividing its circumference by π.

    Example: A circle has a circumference of 12 cm. Find the radius.


    Find the area of circle, given the circumference

    To find the area of a circle when given the circumference, we first use the circumference to find the radius. Then, we use the radius to find the area of the circle.

    Worksheet Calculate problems that involve the radius, diameter, circumference and area of circle. Worksheet 1Word problems that involve circles.
    Worksheet 2 Word problems that involve circles.  
    This video shows how to find the area of a circle given the circumference.


     

    Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


    You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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