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

## Example Questions

### Example Question #1 : 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 #1 : 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 : 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 : 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 #1 : 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 : 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.  