Step by step
The question
Question: a sector has radius 5 cm and angle 72°: 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 72° out of 360°: that is 1/5 of the circle.
part = 72°360° = 15
72 and 360 can both be divided by 72.
72 ÷ 72 = 1, 360 ÷ 72 = 5
2 Whole circle
The area of the whole circle is π r squared: π times 25 is 25π.
circle area = π × 5² = 25π
Careful!
Area uses r squared: 5 times 5.
Not 2 r.
Careful: not π × 5 × 2 = 10π ✗
3 Take the part
Now 1/5 of 25π: 5π.
sector area = 15 × 25π = 5π
In π that is 5π.
As a decimal: about 15.71 cm², to 2 decimal places.
≈ 5π ≈ 15.71 cm²
4 Check
Let's check: 5 slices like this make the whole circle.
5 times 5π is 25π, the whole area.
So it is right!
5 slices: 5 × 5π = 25π
Let's look back.
First: what part of the circle.
Then: whole circle.
Then: take the part.
Last: check.
Answer
≈ 5π ≈ 15.71 cm²