# Basic Geometry : How to find the length of the diameter

## Example Questions

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

Give the diameter of a circle whose circumference is .

Explanation:

### Example Question #115 : Circles

The perimeter of a circle is 36 π.  What is the diameter of the circle?

3

72

36

18

6

36

Explanation:

The perimeter of a circle = 2 πr = πd

Therefore d = 36

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

Two circles have only one point in common. Both circles have radii of . If point  is on the first circle and point  is on the second circle, what is longest possible distance of line ?

12

24

18

6

20

24

Explanation:

The first step is to sketch two circles touching at a single point. In order to maximize the length of , the point and the point would need to be on opposite ends, as shown in the diagram. If the radius of a circle is , then the diameter would be . Therefore, the length of would be .

### Example Question #3 : Diameter

What is the name of the segment in green?

Chord

Diagonal

Diameter

Ray

Diameter

Explanation:

The diameter is the maximum distance between two points on a circle's perimeter. The diameter passes through the circle's center.

### Example Question #4 : Diameter

The area of a circle is .  What is its diameter?

Explanation:

Note that , where is the radius and is the diameter.

Therefore, .

### Example Question #3 : How To Find The Length Of The Diameter

A circle has an area of . What is the circle's diameter?

Explanation:

The area of a circle is given by the equation , where  is the area and  is the radius. Use the given area in this equation and solve for  to find the circle's radius.

To find the circle's diameter, multiply its radius by

### Example Question #4 : How To Find The Length Of The Diameter

A circle has a radius of 7 inches. What is the diameter of the circle?

inches

inches

inches

inches

inches

inches

Explanation:

The diameter of a circle can be written as , where  is the radius and  is the diameter.

Therefore the diameter of the circle is 14 inches.

### Example Question #7 : 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 #8 : Diameter

If the area of a circle is , what is its diameter?

Explanation:

Before we can find the diameter of this circle, we need to find its radius. We need to use the formula for the area of a cirlce:

Given that the area is , we can find the radius

cancel the pi and then square root it to find 'r'.

Now that the radius is found, we can find the diamater by multiplying it by 2.

### Example Question #5 : How To Find The Length Of The Diameter

Find the diameter of a circle that has an area of .

Explanation:

Recall how to find the area of a circle:

Next, plug in the information given by the question.

From this, we can see that we can solve for the radius.

Now recall the relationship between the radius and the diameter.

Plug in the value of the radius to find the diameter.

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