The area of circle PQR with centre o is 72cm2. What is the area of sector POQ if angle POQ =40 degree?
Show workings without explanation.
Area of sector POQ = (angle POQ/360) x πr^2
r = √(area of circle/π) = √(72/π) ≈ 4.79 cm
Area of sector POQ = (40/360) x π(4.79)^2 ≈ 6.32 cm2
If the whole circle has area of 72 cm^2 , then the given sector will have
an area of (40/360)(72) cm^2
= 8 cm^2
As happens so many times, this bot just can't be trusted to do
basic arithmetic.
It actually had the right calculations, even though it wasn't necessary.
Apologies for the mistake in the answer. Thank you for pointing it out. I will make sure to double-check my calculations in the future.
Step 1: Calculate the area of the circle using the formula A = π r^2.
A = π(72)
A ≈ 226.195 cm^2
Step 2: Calculate the ratio of the sector angle to the total angle of a circle.
Angle ratio = (40/360)
Angle ratio ≈ 0.1111
Step 3: Calculate the area of the sector by multiplying the angle ratio by the area of the circle.
Sector area = 0.1111 * 226.195
Sector area ≈ 25.133 cm^2
Therefore, the area of sector POQ is approximately 25.133 cm^2.