Math with Mr. J: Calculating the Circumference of a Circle

Overview

• The lecture focuses on how to calculate the circumference of a circle.
• Two scenarios are covered: given the radius and given the diameter.
• Circumference: The distance around a circle, similar to the perimeter.

Formulas for Circumference

• Circumference using Diameter (d):
  • Formula: ( C = \pi d )
• Circumference using Radius (r):
  • Formula: ( C = 2\pi r )
• Relationship between Diameter and Radius: Diameter is twice the radius, ( d = 2r ).

Understanding Pi (π)

• Pi (π): A constant ratio of a circle's circumference to its diameter.
• Value of Pi: Approximately 3.14, though it is an irrational number.

Example 1: Given Radius

• Scenario: Circle with a radius of 9 centimeters.
• Steps:
  1. Use formula ( C = 2\pi r ).
  2. Plug in the radius: ( C = 2 \times \pi \times 9 ).
  3. Simplify: ( C = 18\pi ) (in terms of pi).
  4. To convert to decimal form, use ( \pi \approx 3.14 ):
     • ( C \approx 2 \times 3.14 \times 9 = 56.52 ) centimeters.

Example 2: Given Diameter

• Scenario: Circle with a diameter of 12 feet.
• Steps:
  1. Use formula ( C = \pi d ).
  2. Plug in the diameter: ( C = \pi \times 12 ).
  3. Simplify: ( C = 12\pi ) (in terms of pi).
  4. To convert to decimal form, use ( \pi \approx 3.14 ):
     • ( C \approx 3.14 \times 12 = 37.68 ) feet.

Conclusion

• Two methods include expressing circumference in terms of pi and using a decimal approximation.
• The video demonstrated using both formulas depending on the given data.
• Emphasized understanding the use of approximate values for calculations involving pi.

• Note: Always be aware of the unit of measure used (e.g., centimeters, feet).