The area of circle PQR with centre O is 72cm2. What is the area of sector POQ if angle POQ=40 degree?
Solve it step by step
Step 1: Find the radius of the circle PQR using the formula A = πr^2, where A is the area of the circle and r is the radius.
72 = πr^2
r^2 = 72/π
r ≈ 4.29 cm
Step 2: Find the area of the sector POQ using the formula A = (θ/360)πr^2, where θ is the central angle in degrees.
A = (40/360)π(4.29)^2
A ≈ 2.28 cm^2
Therefore, the area of sector POQ is approximately 2.28 cm^2.
To find the area of a sector, we need to use the formula:
Area of sector = (θ/360) x πr²
Where:
θ = angle in degrees
r = radius of the circle
Given:
Area of circle PQR = 72 cm²
Angle POQ = 40 degrees
Step 1: Calculate the radius of the circle
Since we know the area of the circle, we can use the formula:
Area of circle = πr²
72 = πr²
Divide both sides of the equation by π:
72/π = r²
Take the square root of both sides:
√(72/π) = r
Step 2: Find the area of the sector
Now that we have the radius (r) and the angle (θ), we can substitute these values into the formula:
Area of sector POQ = (θ/360) x πr²
Area of sector POQ = (40/360) x π(√(72/π))²
Area of sector POQ = (1/9) x π x (√(72/π))²
Area of sector POQ = (1/9) x π x (72/π)
Area of sector POQ = (1/9) x 72
Area of sector POQ = 8 cm²
Therefore, the area of sector POQ is 8 cm².