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.
A quarter of 2 is one half.
So it is half of π times 6.
Half of 6 is 3.
We write it as 3π.
3 Add all the sides
Walk around: the two straight sides, then the curve: 6 + 6 + 3π.
Careful!
The two straight sides are part of the edge too.
Do not add only the curve.
6 plus 6 is 12.
So the perimeter is 12 + 3π.
We keep π in the answer.
That is the exact answer.
4 About how much
To see about how much, put 3.14 for π.
3 times 3.14 is 9.42.
12 plus 9.42 is 21.42.
So the perimeter is about 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.
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.