Radius - Geometry for Kids - What is the radius of a circle? How do we know the radius if we only have the circumference or the area of a circle?
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The radius of a circle is the distance from the center point to the edge of the circle. It's the same distance anywhere on the circle, because the circle has radial symmetry. So it doesn't matter where you measure the radius on the circle, and if you know one radius measurement for a circle, then you know all of them. Try it for yourself and see!

But suppose you *don't* know the radius of this circle? Suppose all you know is that the circumference is 30 centimeters?

One example would be if you were trying to measure a big tree. It would be pretty easy to take a rope and wrap it around the tree, and then measure the length of the rope to find out how big around the tree was (the circumference), but you'd have to cut the tree down to measure the radius. We don't want to cut this big tree down, so we'll need to use math to figure out the radius instead. Luckily we know that the radius of any circle is always the same as half of the circumference divided by π (pi). So the radius of this tree is 30/π = 9.55 centimeters, divided by two is 4.77 centimeters.

How can we be sure that this is true for every circle? Click here for a proof.