PSAT Math : How to find the length of the diameter
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Example Questions
Example Question #1 : 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
16
8
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 #1 : How To Find The Length Of The Diameter
The perimeter of a circle is 36 π. What is the diameter of the circle?
6
36
72
3
18
36
The perimeter of a circle = 2 πr = πd
Therefore d = 36
Example Question #3 : Diameter
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 #1 : 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.
Example Question #31 : Circles
Note: Figure NOT drawn to scale.
In the above circle, the length of arc 
Call the diameter 
Example Question #31 : Circles
Note: Figure NOT drawn to scale.
In the above circle, the length of arc 
Insufficient information exists to answer the question.
Call the diameter 
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