All ACT Math Resources
Example Question #65 : Diameter
Let represent the area of a circle and represent its circumference. Which of the following equations expresses in terms of ?
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?
1. Find the circumference:
2. Find the area:
3. Divide the circumference by the area:
Example Question #2 : How To Find The Ratio Of Diameter And Circumference
How far must a racehorse run in a lap race where the course is a circle with an area of ?
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.