The area of circle PQR with centre o is 72cm2. What is the area of sector POQ if angle POQ is equal to 40 degree?
Write the workings step by step
We are given that the area of circle PQR is 72cm^2.
We know that the formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
So, we can write:
72 = πr^2
Solving for r, we get:
r = sqrt(72/π) ≈ 4.8 cm
Now, we are asked to find the area of sector POQ, where angle POQ = 40°.
The formula for the area of a sector is:
A = (θ/360) x πr^2, where θ is the central angle in degrees.
Substituting θ = 40° and r ≈ 4.8 cm, we get:
A = (40/360) x π x (4.8)^2 ≈ 4.25 cm^2
Therefore, the area of sector POQ is approximately 4.25 cm^2.
1. Start with the formula for the area of a circle: A = πr², where A is the area and r is the radius of the circle.
2. We are given that the area of circle PQR is 72 cm².
3. Rearrange the formula to solve for the radius: r = √(A/π).
4. Substitute the given area into the formula: r = √(72/π) cm.
5. Calculate the value of r using a calculator: r ≈ 4.7958 cm.
6. The sector POQ is a fraction of the entire circle, given by the central angle (40°) divided by 360° (the full angle of a circle).
7. Calculate the fraction: sector fraction = 40° / 360° = 1/9.
8. Multiply the area of the full circle by the sector fraction to find the area of sector POQ: sector area = (1/9) * 72 cm².
9. Simplify the equation: sector area ≈ (1/9) * 72 cm² = 8 cm².
10. Therefore, the area of sector POQ is approximately 8 cm².