The area of circle PQR with centre o is 72cm2. What is the area of sector POQ if angle POQ =40 degree ?
Working without explanation
The area of sector POQ is (40/360) x 72 = 8 cm2.
To find the area of a sector, you can use the formula:
Area of sector = (θ/360) x πr²
Given:
Area of circle = 72 cm²
Angle POQ = 40°
Substituting the given values into the formula:
Area of sector POQ = (40°/360°) x πr²
Simplifying:
Area of sector POQ = (1/9) x πr²
Since the area of the circle is given as 72 cm², we can find the radius using the formula:
Area of circle = πr²
72 = πr²
Dividing both sides by π, we get:
r² = 72/π
Now we can substitute the value of r² into the formula for the area of the sector:
Area of sector POQ = (1/9) x π x (72/π)
Simplifying:
Area of sector POQ = (8/9) x 72
Finally, calculating:
Area of sector POQ = 64 cm²