# GED Math : Radius and Diameter

## Example Questions

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### Example Question #31 : 2 Dimensional Geometry

What is the radius of a circle if it has a circumference of ?

Explanation:

In order to solve this problem, it's important to understand the relationship between the two terms mentioned: radius and circumference.

The circumference of a circle can be solved for with the formula: , where r is radius. By substituting the circumference value into the equation, we should be able to solve for the radius fairly quickly.

Therefore, the radius of the circle is

### Example Question #32 : 2 Dimensional Geometry

If a circle has an area of , what is its diameter?

Explanation:

When it comes to circles, it's especially helpful to try and think about how things relate. This problem only provides the area of the circle, but it's asking for the diameter. How do these two things relate?

Well, the formula for area of a circle is given by: , where r is the radius.

The diameter of a circle can be solved for via: , where r is the radius.

Therefore, we see that two concepts are related through radius. This means that with the area, we can solve for radius. And then, we can use the radius to solve for the diameter.

Now, we may solve for the diameter.

Therefore, the diameter of the circle is

### Example Question #33 : 2 Dimensional Geometry

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

Explanation:

When it comes to circles, it's especially helpful to try and think about how things relate. This problem only provides the area of the circle, but it's asking for the diameter. How do these two things relate?

Well, the formula for area of a circle is given by: , where r is the radius.

The diameter of a circle can be solved for via: , where r is the radius.

Therefore, we see that two concepts are related through radius. This means that with the area, we can solve for radius. And then, we can use the radius to solve for the diameter.

Now, we may solve for the diameter.

Therefore, the diameter of the circle is

### Example Question #34 : 2 Dimensional Geometry

If a circle has an area of , what is its diameter?

Explanation:

When it comes to circles, it's especially helpful to try and think about how things relate. This problem only provides the area of the circle, but it's asking for the diameter. How do these two things relate?

Well, the formula for area of a circle is given by: , where r is the radius.

The diameter of a circle can be solved for via: , where r is the radius.

Therefore, we see that two concepts are related through radius. This means that with the area, we can solve for radius. And then, we can use the radius to solve for the diameter.

Now, we may solve for the diameter.

Therefore, the diameter of the circle is

### Example Question #35 : 2 Dimensional Geometry

If a circle has an area of , what is its radius?

Explanation:

When it comes to circles, it's a great strategy to think about how concepts are related. In this problem the area is provided, but you are asked to solve for the area. But how are these two concepts related?

Well, area is solved for by: , where r is the radius.

This means that we can directly solve for radius through substituting in the value for the area.

Remember that you need to take the square root in order to solve for r.

### Example Question #36 : 2 Dimensional Geometry

What is the radius of a circle if it has an area of ?

Explanation:

When it comes to circles, it's a great strategy to think about how concepts are related. In this problem the area is provided, but you are asked to solve for the area. But how are these two concepts related?

Well, area is solved for by: , where r is the radius.

This means that we can directly solve for radius through substituting in the value for the area.

Remember that you need to take the square root in order to solve for r.

### Example Question #37 : 2 Dimensional Geometry

Find the radius of a circle with an area of .

Explanation:

When it comes to circles, it's a great strategy to think about how concepts are related. In this problem the area is provided, but you are asked to solve for the area. But how are these two concepts related?

Well, area is solved for by: , where r is the radius.

This means that we can directly solve for radius through substituting in the value for the area.

Remember that you need to take the square root in order to solve for r.

### Example Question #38 : 2 Dimensional Geometry

Your school as a circular lobby. If the distance around the outside of the lobby is , what is the distance across the widest part of the floor?

Explanation:

Your school as a circular lobby. If the distance around the outside of the lobby is , what is the distance across the widest part of the floor?

This question is asking us for diameter. We know this because we are told to find the distance across the widest part of a circular shape. The widest part of a circle will always go through the center, and assuming a straight line, will be its diameter.

To find the diameter, we can work backward from our circumference formula:

Now, we know that

So, we can rewrite our C formula to get:

So, now we can solve for our diameter pretty easily!

### Example Question #39 : 2 Dimensional Geometry

Use 3.14 for pi.

What is the radius of a circle with a circumference of 169.56 ft?

Explanation:

First we need to recall that the formula for circumference of a circle is:

Where  is circumference and  is diameter

We are given the circumference, and told to use 3.14 for pi, so we can plug these into our equation and solve for diameter

we divide both sides by 3.14

Now that we have our diameter we need to divide it by 2 to find our radius

### Example Question #40 : 2 Dimensional Geometry

What is the radius, in inches, of a circle with a diameter of 12 inches?