Distinguishing Circumference and Area

Student Summary

Sometimes we need to find the circumference of a circle, and sometimes we need to find the area.

Here are some examples of quantities related to the circumference of a circle:

  • The length of a circular path.
  • The distance a wheel will travel after one complete rotation.
  • The length of a piece of rope coiled in a circle.

Here are some examples of quantities related to the area of a circle:

  • The amount of land that is cultivated on a circular field.
  • The amount of frosting needed to cover the top of a round cake.
  • The number of tiles needed to cover a round table.

In both cases, the radius (or diameter) of the circle is all that is needed to make the calculation. The circumference of a circle with radius rr is 2πr2\pi r while its area is πr2\pi r^2. The circumference is measured in linear units (such as cm, in, km) while the area is measured in square units (such as cm2, in2, km2).

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