### All High School Math Resources

## Example Questions

### Example Question #131 : Plane Geometry

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

**Possible Answers:**

**Correct answer:**

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 #1 : 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?

**Possible Answers:**

4

2

8

32

16

**Correct answer:**

16

Set the area of the circle equal to four times the circumference *πr*^{2} = 4(2*πr*).

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?

**Possible Answers:**

18

6

72

3

36

**Correct answer:**

36

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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 = πr^{2}.