Step by step
The question
Question: a sector has radius 3 cm and angle 180°: 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 180° out of 360°: that is 1/2 of the circle.
part = 180°360° = 12
180 and 360 can both be divided by 180.
180 ÷ 180 = 1, 360 ÷ 180 = 2
2 Whole circle
The area of the whole circle is π r squared: π times 9 is 9π.
circle area = π × 3² = 9π
Careful!
Area uses r squared: 3 times 3.
Not 2 r.
Careful: not π × 3 × 2 = 6π ✗
3 Take the part
Now 1/2 of 9π: 9π over 2.
sector area = 12 × 9π = 9π2
In π that is 9π over 2.
As a decimal: about 14.14 cm², to 2 decimal places.
≈ 9π2 ≈ 14.14 cm²
4 Check
Let's check: 2 slices like this make the whole circle.
2 times 9π over 2 is 9π, the whole area.
So it is right!
2 slices: 2 × 9π2 = 9π
Let's look back.
First: what part of the circle.
Then: whole circle.
Then: take the part.
Last: check.
Answer
≈ 9π2 ≈ 14.14 cm²