Step by step
The question
Question: a sector has radius 12 cm and angle 150°: 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 150° out of 360°: that is 5/12 of the circle.
part = 150°360° = 512
150 and 360 can both be divided by 30.
150 ÷ 30 = 5, 360 ÷ 30 = 12
2 Whole circle
The area of the whole circle is π r squared: π times 144 is 144π.
circle area = π × 12² = 144π
Careful!
Area uses r squared: 12 times 12.
Not 2 r.
Careful: not π × 12 × 2 = 24π ✗
3 Take the part
Now 5/12 of 144π: 60π.
sector area = 512 × 144π = 60π
In π that is 60π.
As a decimal: about 188.5 cm², to 2 decimal places.
≈ 60π ≈ 188.5 cm²
4 Check
Let's check: the whole is 12/5 times the part: 144π again.
So it is right!
125 × 60π = 144π
Let's look back.
First: what part of the circle.
Then: whole circle.
Then: take the part.
Last: check.
Answer
≈ 60π ≈ 188.5 cm²