the area of a circle PQR with centre O is 72 cm square. what is the area of sector POQ if angle POQ is equal to 40 degree?
40/360=
1/9
1/9*72
=8cm squared
The area of a circle PQR with centre O is 72cmsquare.What is the area of sector PQR,if angle PQR=40degree
A=40/360×72
A=8cm²
by PQR do you mean a sector? Generally circles are not described using three points.
Anyway, the area of a sector is
a = 1/2 r^2 θ
That is also my question
Who can solve it for me
Area of a sector=Angle÷ 360×π r×r
40÷360×22÷7×72×72
Pls continue from there
Area of circle=72cm square
Acircle=3.142×rsquare
72=3.142×r square
r square=72\3.142
r square=22.91
SQUARE ROOT BOTH SIDES
Square root r square=square root 22.91
r=4.78~4.8
Asector=40/360×3.142×4.8 square
Asector=2895.6672/360
Asector=8.04352cm square~8cm square
To find the area of a sector, you need to use the formula:
Area of sector = (θ/360) * π * r²
Where:
- θ is the central angle of the sector (measured in degrees).
- π (pi) is a mathematical constant approximately equal to 3.14159.
- r is the radius of the circle.
In this case, you are given the area of the whole circle as 72 cm², and you need to find the area of sector POQ with a central angle of 40 degrees.
To find the radius of the circle, you can use the formula:
Area of circle = π * r²
Rearranging the formula, we get:
r² = (Area of circle) / π
Substituting the given area of the circle as 72 cm², we can calculate the radius:
r² = 72 / π
r² ≈ 22.92 (rounded to two decimal places)
r ≈ √22.92
r ≈ 4.79 cm (rounded to two decimal places)
Now that we have the radius, we can calculate the area of sector POQ:
Area of sector = (40/360) * π * (4.79)²
Area of sector ≈ 0.1111 * π * 22.92
Area of sector ≈ 0.1111 * 71.91
Area of sector ≈ 7.987 cm² (rounded to three decimal places)
Therefore, the area of sector POQ with a central angle of 40 degrees is approximately 7.987 cm².