Step by step
The question
Question: a sector has radius 6 cm and angle 120°: 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 is 360°.
The slice is 120° out of 360°: that is 1/3 of the circle.
part = 120°360° = 13
120 and 360 can both be divided by 120.
120 ÷ 120 = 1, 360 ÷ 120 = 3
2 Whole circle
The area of the whole circle is π r squared: π times 36 is 36π.
circle area = π × 6² = 36π
Careful!
Area uses r squared: 6 times 6.
Not 2 r.
Careful: not π × 6 × 2 = 12π ✗
3 Take the part
Now 1/3 of 36π: 12π.
sector area = 13 × 36π = 12π
In π that is 12π.
As a decimal: about 37.7 cm², to 2 decimal places.
≈ 12π ≈ 37.7 cm²
4 Check
Let's check: 3 slices like this make the whole circle.
3 times 12π is 36π, the whole area.
So it is right!
3 slices: 3 × 12π = 36π
Let's look back.
First: what part of the circle.
Then: whole circle.
Then: take the part.
Last: check.
Answer
≈ 12π ≈ 37.7 cm²