# Finding the Radius: Formula & Concept

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• 0:04 What Is the Radius?
• 0:36 What About the Diameter?
• 3:14 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In some problems, the radius is easy to spot, but in others, the radius requires the use of some formulas. Learn how the formulas for circumference and area can help you in figuring out the radius of a circle or sphere.

So, what exactly is the radius? The radius tells you how big a particular circle is. It starts at the center of a circle and goes to the edge of the circle. How long the radius is determines how large the circle is. A larger radius means a larger circle.

Notice that a smaller circle has a shorter, or smaller, radius than a larger circle. You can test it for yourself, too. Find any two circles of different sizes and measure their radiuses and compare. Which radius is larger? Which is smaller?

There's another term related to the radius that you need to know, and that is diameter. The diameter is twice as long as the radius and is the distance from edge to edge of the circle passing through the center. If the radius is 2 inches long, then the diameter will be 4 inches long. It's always double. Let us now see how the various formulas for circles will help us find the radius.

## Finding the Radius Using Circumference

We've just been given the circumference of a particular circle, and we now need to find the radius of the circle. How do we proceed?

First, we need the formula for circumference, which is C=2*pi*r. Once we have the formula, we can plug in our numbers for circumference and the constant pi to solve for r. We will use our algebra skills to rewrite the equation so r is by itself. Follow along with our steps.

We start with our circumference formula, which is C = 2*pi*r. Our next step is plugging in all the numbers we know. We know the circumference is 8 and we know the constant pi is always 3.14. After that, we simplify by multiplying the 2 by pi. After that, we divide by 6.28 so that r is by itself. When r is by itself, we have solved for the radius and now know how large the radius is. In this case, our radius is 1.27 meters.

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