The area of circle PQR with centre o is 72cm2. What is the area of sector POQ if angle POQ =40
Bring out the workings without explanation
Area of sector POQ = (40/360) x πr²
r² = 72/π
r = √(72/π)
Area of sector POQ = (40/360) x π x (√(72/π))²
= (2/9) x 72
= 16cm²
Step 1: Determine the formula for the area of a sector.
Area of a sector = (θ/360) * πr²
Step 2: Plug in the given values.
Area of sector POQ = (40/360) * π * r²
Step 3: Simplify the equation.
Area of sector POQ = (1/9) * π * r²
Step 4: Substitute the given area of circle PQR.
72 = π * r²
Step 5: Solve for r.
r² = 72/π
r² ≈ 22.92
r ≈ √22.92
Step 6: Substitute the value of r into the equation for the area of sector POQ.
Area of sector POQ ≈ (1/9) * π * 22.92
Area of sector POQ ≈ 8.05 cm²