SAT 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?
32
4
16
2
8
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 : Diameter
The perimeter of a circle is 36 π. What is the diameter of the circle?
3
36
72
18
6
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 #5 : 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 #5 : Diameter
The circumference of the circle is 
Write the formula for the circumference.
Substitute the circumference.
Example Question #6 : Diameter
Find the diameter of a circle whose area is 
To solve, simply use the formula for the area of a circle to find the radius, and then multiply it by 2 to find the diameter. Thus,
Example Question #5 : How To Find The Length Of The Diameter
Find the length of the diameter given radius of 1.
To solve, simply use the formula for the diameter of a circle. Thus,
Example Question #6 : How To Find The Length Of The Diameter
Find the length of the diameter given the radius is 5.
To solve, simply use the formula for the diameter of a circle
where r is 5. Thus,
Remember, the diameter is the longest distance across a circle, and since the radius is 5, you can simply double that. Thus, the answer is 10.
Example Question #1 : How To Find The Length Of The Diameter
Find the diameter of a circle given the radius is 6.
To solve, simply use the formula for the diameter of circle.
Remember, since the diameter is distance between two points on opposite sides of the circle, you simply double the radius. No pi is involved in diameter, only in circumference, area, etc.
Example Question #1 : How To Find The Length Of The Diameter
The circumference of a given circle is half of its area. What is the diameter of the circle?
Remember that the circumference of a circle is given by 
If the circumference of this circle if one half its area, then we can say 
We can solve this equation for r like so:
Since the diameter of a circle is twice its radius, then the diameter of this circle is 8.
To check your answer, plug in r=4 into the circumference and area formulas. You will see that the area of this circle is 
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