Perimeter of a quarter circle radius 6 Step by Step

Step by step

The question

Question: find the perimeter of a quarter circle with radius 6.

1 Find the edge

The perimeter is the way all around the edge.

A quarter circle has two straight sides, the radii,

and one curve.

Each straight side is 6.

2 The curve

The curve is a quarter of the way round a circle.

The way round a circle is 2 times π times r.

We take a quarter.

curve = 14 × 2 × π × 6

A quarter of 2 is one half.

14 × 2 = 12

So it is half of π times 6.

curve = 12 × π × 6

Half of 6 is 3.

We write it as 3π.

curve = 3π

3 Add all the sides

Walk around: the two straight sides, then the curve: 6 + 6 + 3π.

P = 6 + 6 + 3π

Careful!

The two straight sides are part of the edge too.

Do not add only the curve.

Careful: not P = 3π ✗

6 plus 6 is 12.

So the perimeter is 12 + 3π.

We keep π in the answer.

That is the exact answer.

P = 12 + 3π

4 About how much

To see about how much, put 3.14 for π.

P ≈ 12 + 3 × 3.14

3 times 3.14 is 9.42.

P ≈ 12 + 9.42

12 plus 9.42 is 21.42.

So the perimeter is about 21.42.

P ≈ 21.42

5 Check

Let's check the curve.

Going round the corner of the square instead is 6 + 6 = 12.

The curve is about 9.42.

It is longer than one straight side: 6.

It is shorter than going round the corner: 12.

6 < 9.42 < 12

So the answer makes sense!

Let's look back.

First: find the edge.

Then: the curve.

Then: add all the sides.

Then: about how much.

Last: check.

Answer