Step by step
The question
Question: a sector has radius 8 cm and angle 300°: 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 300° out of 360°: that is 5/6 of the circle.
part = 300°360° = 56
300 and 360 can both be divided by 60.
300 ÷ 60 = 5, 360 ÷ 60 = 6
2 Whole circle
The area of the whole circle is π r squared: π times 64 is 64π.
circle area = π × 8² = 64π
Careful!
Area uses r squared: 8 times 8.
Not 2 r.
Careful: not π × 8 × 2 = 16π ✗
3 Take the part
Now 5/6 of 64π: 160π over 3.
sector area = 56 × 64π = 160π3
In π that is 160π over 3.
As a decimal: about 167.55 cm², to 2 decimal places.
≈ 160π3 ≈ 167.55 cm²
4 Check
Let's check: the whole is 6/5 times the part: 64π again.
So it is right!
65 × 160π3 = 64π
Let's look back.
First: what part of the circle.
Then: whole circle.
Then: take the part.
Last: check.
Answer
≈ 160π3 ≈ 167.55 cm²