the area of a circle pqr with a center o is 72cm2 what is the area of sector poq if poq = 40 degree
40 = 360/9
so, 1/9 of the whole area.
To find the area of a sector, you need to know the radius of the circle and the central angle of the sector.
In this case, we are given that the area of the circle is 72 cm^2. The formula for the area of a circle is A = πr^2, where A represents the area and r represents the radius.
To find the radius of the circle, you can rearrange the formula for the area of a circle:
A = πr^2
Divide both sides of the equation by π:
A/π = r^2
Take the square root of both sides to solve for r:
√(A/π) = r
Substitute the given area value into the equation:
√(72/π) = r
Now that we have the radius, we can find the area of the sector.
The formula for the area of a sector is A_sector = (θ/360) * πr^2, where θ represents the central angle of the sector.
In this case, we are given that θ (POQ) is 40 degrees.
Substitute the values into the formula:
A_sector = (40/360) * π * (radius)^2
Calculate the area of the sector using the given radius:
A_sector = (40/360) * π * (√(72/π))^2
Simplify:
A_sector = (40/360) * π * (8/√π)^2
A_sector = (40/360) * π * (64/π)
Simplify further:
A_sector = (40/360) * 64
A_sector = (4/36) * 64
A_sector = 256/36
Simplify or convert to a decimal:
A_sector ≈ 7.11 cm^2
Therefore, the area of sector POQ is approximately 7.11 cm^2.