The area of circle PQR with centre o is 72cm2. What is the area of sector POQ if angle POQ =40 degree?
Workings without explanation
Area of sector POQ = (40/360) x 72 = 8 cm2.
Step 1: Calculate the area of the entire circle PQR.
Area of a circle = πr², where r is the radius.
Given that the area of circle PQR is 72cm², we can use the formula to find the radius.
72 = πr²
Step 2: Solve for the radius.
Divide both sides of the equation by π:
72/π = r²
Step 3: Take the square root of both sides to find the radius.
√(72/π) = r
Step 4: Calculate the area of sector POQ.
Area of sector POQ = (angle POQ/360°) * area of the entire circle
= (40/360) * (πr²)
= (1/9) * (πr²)
Step 5: Substitute the value of the radius from Step 3 into the formula.
Area of sector POQ = (1/9) * (π * √(72/π)²)
= (1/9) * (π * (72/π))
= 8π cm²
Therefore, the area of sector POQ is 8π cm².