Circle circumference 10π, find the radius Step by Step

Step by step

The question

Question: find the radius r of a circle with circumference 10π.

1 Write the rule

The circumference is 2 times π times the radius: C = 2 × π × r.

Now put the numbers in: C = 10π.

2 × π × r = 10π

Careful!

10 is the diameter.

The radius is half of it.

Careful: not r = 10 ✗

2 Remove the π

π is on both sides.

So we divide both sides by π.

We do it on both sides.

Why both sides?

The = sign means both sides are the same amount.

If we change only one side, they are not the same any more.

2 × π × rπ = 10ππ

π divided by π is 1.

Now we have 2 × r = 10.

2 × r = 10

3 Remove the × 2

To remove times 2, we divide by 2.

We do it on both sides, so they stay equal.

2 × r2 = 102

2 divided by 2 is 1.

So just r is left.

10 divided by 2 is 5.

So the radius is 5.

r = 5

4 Check

Let's check: put r = 5 back in the rule.

2 × π × 5 = 10π

We get 10π again.

So the radius is right!

Let's look back.

First: write the rule.

Then: remove the π.

Then: remove the × 2.

Last: check.

Answer