Perimeter of a quarter circle radius 10 Step by Step

Step by step

The question

Question: find the perimeter of a quarter circle with radius 10.

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 10.

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 × 10

A quarter of 2 is one half.

14 × 2 = 12

So it is half of π times 10.

curve = 12 × π × 10

Half of 10 is 5.

We write it as 5π.

curve = 5π

3 Add all the sides

Walk around: the two straight sides, then the curve: 10 + 10 + 5π.

P = 10 + 10 + 5π

Careful!

The two straight sides are part of the edge too.

Do not add only the curve.

Careful: not P = 5π ✗

10 plus 10 is 20.

So the perimeter is 20 + 5π.

We keep π in the answer.

That is the exact answer.

P = 20 + 5π

4 About how much

To see about how much, put 3.14 for π.

P ≈ 20 + 5 × 3.14

5 times 3.14 is 15.7.

P ≈ 20 + 15.7

20 plus 15.7 is 35.7.

So the perimeter is about 35.7.

P ≈ 35.7

5 Check

Let's check the curve.

Going round the corner of the square instead is 10 + 10 = 20.

The curve is about 15.7.

It is longer than one straight side: 10.

It is shorter than going round the corner: 20.

10 < 15.7 < 20

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