Perimeter of a quarter circle radius 4 m Step by Step

Step by step

The question

Question: find the perimeter of a quarter circle with radius 4 m.

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 4 m.

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 × 4

A quarter of 2 is one half.

14 × 2 = 12

So it is half of π times 4.

curve = 12 × π × 4

Half of 4 is 2.

We write it as 2π.

curve = 2π m

3 Add all the sides

Walk around: the two straight sides, then the curve: 4 + 4 + 2π.

P = 4 + 4 + 2π

Careful!

The two straight sides are part of the edge too.

Do not add only the curve.

Careful: not P = 2π ✗

4 plus 4 is 8.

So the perimeter is 8 + 2π.

We keep π in the answer.

That is the exact answer.

P = 8 + 2π m

4 About how much

To see about how much, put 3.14 for π.

P ≈ 8 + 2 × 3.14

2 times 3.14 is 6.28.

P ≈ 8 + 6.28

8 plus 6.28 is 14.28.

So the perimeter is about 14.28 m.

P ≈ 14.28 m

5 Check

Let's check the curve.

Going round the corner of the square instead is 4 + 4 = 8.

The curve is about 6.28.

It is longer than one straight side: 4.

It is shorter than going round the corner: 8.

4 < 6.28 < 8

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