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 #1 :How To Find The Length Of The Diameter
If the area of a circle is four times larger than the circumference of that same circle, what is the diameter of the circle?
32
4
2
16
8
16
Set the area of the circle equal to four times the circumferenceπr2= 4(2πr).
Cross out bothπsymbols and oneron each side leaves you withr= 4(2) sor= 8 and therefored= 16.
Example Question #1 :How To Find The Length Of The Diameter
The perimeter of a circle is 36 π. What is the diameter of the circle?
36
18
72
6
3
36
The perimeter of a circle = 2 πr = πd
Therefore d = 36
Example Question #2 :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 #2 :How To Find The Length Of The Diameter
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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