# High School Math : How to find the length of the diameter

## Example Questions

### Example Question #1 : How To Find The Length Of The Diameter

What is the diameter of a circle with a circumference of ?     Explanation:

To find the diameter we must understand the diameter in terms of circumference. The equation for the circumference of a circle is , where is the circumference and is the diameter. The circumference is equal to the diameter multiplied by .

We can rearrange to solve for . All we have to do is plug in the circumference and divide by , and it will yield the diameter. The s cancel and the diameter is .

### Example Question #31 : Circles

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

2

16

32

8

16

Explanation:

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 = 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

3

72

18

36

36

Explanation:

The perimeter of a circle = 2 πr = πd

Therefore d = 36

### Example Question #2 : How To Find The Length Of The Diameter If the area of the circle touching the square in the picture above is , what is the closest value to the area of the square?      Explanation:

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 , , and . The radii of the circle (from the center to the corners of the square) will be 9. The hypotenuse (side of the square) must be .

The area of the square is then .

### Example Question #1 : Diameter

Two legs of a right triangle measure 3 and 4, respectively. What is the area of the circle that circumscribes the triangle?        