High School Math : Plane Geometry
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Example Questions
Example Question #131 : Plane Geometry
A circle has a diameter of 13 cm. What is the circle's circumference?
To find the circumference of a circle, multiply the circle's diameter by 
Example Question #12 : How To Find Circumference
Find the circumference of the following circle:
The formula for the circumference of a circle is
where 
Plugging in our values, we get:
Example Question #345 : Plane Geometry
A car tire has a radius of 18 inches. When the tire has made 200 revolutions, how far has the car gone in feet?
500π
300π
600π
3600π
600π
If the radius is 18 inches, the diameter is 3 feet. The circumference of the tire is therefore 3π by C=d(π). After 200 revolutions, the tire and car have gone 3π x 200 = 600π feet.
Example Question #51 : Plane Geometry
A circle has the equation below. What is the circumference of the circle?
(x – 2)2 + (y + 3)2 = 9
The radius is 3. Yielding a circumference of 
Example Question #301 : Circles
Ashley has a square room in her apartment that measures 81 square feet. What is the circumference of the largest circular area rug that she can fit in the space?
In order to solve this question, first calculate the length of each side of the room.
The length of each side of the room is also equal to the length of the diameter of the largest circular rug that can fit in the room. Since 
Example Question #1 : How To Find The Length Of The Diameter
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 : 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.
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