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.
What Is the Radius?
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?
What About the Diameter?
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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If given the area of a circle, we would find the radius using a similar procedure as that of the circumference. We would plug values into the formula for area and then solve for r.
Let's say we're given an area of 9.27 inches squared and are asked to find the radius of a circle. Let's see how we would proceed. The equation for area is A=pi*r^2. To solve this equation for r, we use our algebra skills again to reverse each step. Wherever we see multiplication, we will do division. Where we see a value squared, we will do a square root. Follow along with these steps.
We start with our area formula, which is A = pi*r^2. We plug in the values that we know and, in this case, we know the area equals 9.27, and we know that pi equals 3.14. Next we work to get r by itself by dividing both sides by 3.14, which leaves us with 9.27 / 3.14 = r^2. This leaves us with 2.95 = r^2, and, to get r by itself, we have to find the square root of both sides. This leaves us with r equals the square root of 2.95, and when we calculate this, we learn that r = 1.72 inches.
The two formulas that are useful for finding the radius of a circle are C=2*pi*r and A=pi*r^2. We use algebra skills in solving for our variable r. We know that the constant pi is always 3.14. Another word related to the radius is diameter, which is always twice the radius.
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