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# LESSON: Circumference of Circles

## Find the Diameter or Radius of a Circle Given Circumference

What happens if you are given the circumference but not the radius or the diameter? Can you still solve for one or the other?

Working in this way is a bit tricky and will require us to work as detectives once again. You will have to work backwards to figure out the radius and/or the diameter when given only the circumference to work with.

Example 1

Find the diameter of a circle with a circumference of 21.98 feet.

To work on this problem, we will need our formula for finding the circumference of a circle.

$C = \pi d$

Next, we fill in the given information.

$21.98 = (3.14)d$

To solve this problem we need to figure out what times 3.14 will give us 21.98. To do this, we divide 21.98 by 3.14.

${3.14 \overline{ ) {21.98 \;}}}$

Remember dividing decimals? First, we move the decimal point two places to make our divisor a whole number. Then we can divide as usual.

$& \overset{ \qquad \ \quad 7}{314 \overline{ ) {2198}}}$

The diameter of this circle is 7 feet.

How could we figure out the radius once we know the diameter?

We can figure out the radius by dividing the diameter in half. The radius is one-half the measure of the diameter.

7 $\div$ 2 $=$ 3.5

The radius of the circle is 3.5 feet.