ACT Math : How to find the ratio of diameter and circumference

Example Questions

Example Question #1 : How To Find The Ratio Of Diameter And Circumference

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 #11 : Diameter

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 #12 : Diameter

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.