High School Math : How to find the length of the diameter
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Example Questions
Example Question #1 : Diameter And Chords
What is the diameter of a circle with a circumference of 
To find the diameter we must understand the diameter in terms of circumference. The equation for the circumference of a circle is 
We can rearrange 
All we have to do is plug in the circumference and divide by 
The 
Example Question #2 : Diameter And Chords
If the area of a circle is four times larger than the circumference of that same circle, what is the diameter of the circle?
4
32
8
16
2
16
Set the area of the circle equal to four times the circumference πr2 = 4(2πr).
Cross out both π symbols and one r on each side leaves you with r = 4(2) so r = 8 and therefore d = 16.
Example Question #2 : Diameter
The perimeter of a circle is 36 π. What is the diameter of the circle?
18
3
72
36
6
36
The perimeter of a circle = 2 πr = πd
Therefore d = 36
Example Question #3 : Diameter And Chords
If the area of the circle touching the square in the picture above is 
Obtain the radius of the circle from the area.
Split the square up into 4 triangles by connecting opposite corners. These triangles will have a right angle at the center of the square, formed by two radii of the circle, and two 45-degree angles at the square's corners. Because you have a 45-45-90 triangle, you can calculate the sides of the triangles to be 
The area of the square is then 
Example Question #4 : Diameter And Chords
Two legs of a right triangle measure 3 and 4, respectively. What is the area of the circle that circumscribes the triangle?
For the circle to contain all 3 vertices, the hypotenuse must be the diameter of the circle. The hypotenuse, and therefore the diameter, is 5, since this must be a 3-4-5 right triangle.
The equation for the area of a circle is A = πr2.
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