Step by step
The question
Question: a sector has radius 9 cm and angle 40°: find the area of the sector.
A sector is a slice of the circle, like a slice of pizza.
1 What part of the circle
A whole turn around the middle is 360°.
A bigger angle cuts a bigger slice.
The slice is 40° of the 360°: 40/360.
To make it simpler: 40 goes into 360: 40 × 9 = 360.
So 40 goes into both.
So we divide the top and the bottom by 40.
That is 1/9 of the circle.
2 Whole circle
The area of the whole circle is π times r squared.
9 times 9 is 81.
So it is 81π.
Careful!
Area uses r squared: 9 times 9.
Not 2 r.
3 Take the part
The slice is 1/9 of the whole circle.
"Of" means times.
Cut the whole into 9 equal parts.
One part is 81 divided by 9: 9.
The π stays.
So it is 9π.
With a calculator, π is 3.14159 and more.
9 times π is about 28.27, to 2 decimal places.
So the area is 9π, about 28.27 cm².
4 Check
Let's check: 9 slices like this make the whole circle.
9 times 9π is 81π, the whole area.
So it is right!
Let's look back.
First: what part of the circle.
Then: whole circle.
Then: take the part.
Last: check.