The area of circle PQR with centre O is 72cmsquared.what is the area of sector PQR,if POR
=40squared
I can't quite picture your diagram, but 40 is 5/9 of the whole area. Maybe you can use that to get what you're after.
To find the area of a sector, you need to find the proportion of the angle of the sector to the full angle of the circle and multiply it by the area of the whole circle.
1. Calculate the area of the whole circle:
The area of a circle is given by the formula A = πr^2.
Given that the area of circle PQR is 72 cm^2, we can use the formula to find the radius (r).
A = πr^2
72 = πr^2
r^2 = 72/π
r ≈ √(72/π)
Calculate the approximate value of the radius.
2. Calculate the angle of the sector:
We know that POR = 40^2.
Therefore, the angle of sector PQR is 40^2°.
3. Calculate the proportion of the angle:
To find the proportion, divide the given angle of the sector by the full angle of the circle (360°):
Proportion = (angle of sector PQR) / 360
4. Calculate the area of the sector:
To find the area of the sector, multiply the proportion obtained in step 3 by the area of the whole circle:
Area of sector PQR = Proportion * Area of circle PQR
Plug in the values you have calculated to find the final answer.