# PSAT Math : How to find the length of the diameter

## Example Questions

### 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

8

4

16

2

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?

36

3

6

18

72

36

Explanation:

The perimeter of a circle = 2 πr = πd

Therefore d = 36

### Example Question #1 : 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 : 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?

Explanation:

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 #1 : Diameter And Chords

Note: Figure NOT drawn to scale.

In the above circle, the length of arc  is , and . What is the diameter of the circle?

Explanation:

Call the diameter . Since  is  of the circle, and  is  of a circle with circumference .

is  in length, so

### Example Question #1 : Diameter And Chords

Note: Figure NOT drawn to scale.

In the above circle, the length of arc  is 10, and . Give the diameter of the circle. (Nearest tenth).