# ISEE Upper Level Math : How to find the length of a radius

## Example Questions

### Example Question #1 : How To Find The Length Of A Radius

What is the radius of a circle with circumference equal to ?

Explanation:

The circumference of a circle can be found using the following equation:

### Example Question #2 : How To Find The Length Of A Radius

What is the value of the radius of a circle if the area is equal to ?

Explanation:

The equation for finding the area of a circle is

Therefore, the equation for finding the value of the radius in the circle with an area of  is:

### Example Question #3 : How To Find The Length Of A Radius

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

Explanation:

The circumference of a circle can be found using the following equation:

We plug in the circumference given,  into  and use algebraic operations to solve for .

### Example Question #4 : How To Find The Length Of A Radius

Refer to the above diagram.  has length . Give the radius of the circle.

Explanation:

Inscribed , which measures , intercepts a minor arc with twice its measure. That arc is , which consequently has measure

.

The corresponding major arc, , has as its measure

, and is

of the circle.

If we let  be the circumference and  be the radius, then  has length

.

This is equal to , so we can solve for  in the equation

The radius of the circle is 50.

### Example Question #5 : How To Find The Length Of A Radius

A circle has a circumference of . What is the radius of the circle?

Not enough information to determine.

Explanation:

A circle has a circumference of . What is the radius of the circle?

Begin with the formula for circumference of a circle:

Now, plug in our known and work backwards:

Divide both sides by two pi to get:

### Example Question #6 : How To Find The Length Of A Radius

You are exploring the woods near your house, when you come across an impact crater. It is perfectly circular, and you estimate its area to be .

What is the radius of the crater?

Cannot be determined from the information provided

Explanation:

You are exploring the woods near your house, when you come across an impact crater. It is perfectly circular, and you estimate its area to be .

What is the radius of the crater?

To solve this, we need to recall the formula for the area of a circle.

Now, we know A, so we just need to plug in and solve for r!

Begin by dividing out the pi

Then, square root both sides.