## Example Questions

### Example Question #111 : Circles

Let represent the area of a circle and represent its circumference. Which of the following equations expresses in terms of       Explanation:

The formula for the area of a circle is , and the formula for circumference is . If we solve for C in terms of r, we get .

We can then substitute this value of r into the formula for the area:    ### Example Question #1 : How To Find The Ratio Of Diameter And Circumference

A circle has a radius of . What is the ratio of its circumference to its area?      Explanation:

1. Find the circumference:  2. Find the area:  3. Divide the circumference by the area: ### Example Question #531 : Plane Geometry

How far must a racehorse run in a lap race where the course is a circle with an area of ?      Explanation:

To find the answer, we need to first find the circumference of the circle then mulitply that by 4 because the racehorse is running 4 laps.

We know that the area of the circle is . We can then find the radius.    Because , our diameter is 12.

We can now find the circumference.  Multiply the circumference by 4 (our racehorse is running 4 laps) to find the answer. ### All ACT Math Resources 