An arc of a circle of radius 10cm subtends an angle 120° at a center a circle. Calculate the area of the sector OAB
a = 1/2 r^2 θ = 1/2 * 10^2 * 2π/3 = 100π/3 cm^2
6.6 cm
To calculate the area of the sector OAB, we can use the formula:
Area = (θ/360) * π * r^2
where θ is the central angle of the sector and r is the radius of the circle.
In this case, the central angle is 120° and the radius is 10 cm. Substituting these values into the formula, we get:
Area = (120/360) * π * 10^2
Simplifying:
Area = (1/3) * π * 100
Area = (1/3) * 3.14 * 100
Area = 104.67 cm²
Therefore, the area of the sector OAB is approximately 104.67 square centimeters.
To calculate the area of the sector OAB, we can use the formula:
Area = (θ/360°) * π * r^2
Where θ is the angle subtended by the sector (in radians), π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
In this case, the angle θ is 120° and the radius r is 10cm. However, we need to convert the angle from degrees to radians before using the formula.
To convert degrees to radians, we use the following formula:
Radians = (π/180°) * degrees
Using this formula, we can convert 120 degrees to radians:
Radians = (π/180°) * 120°
= (π/180) * 120/1
= (π/3) radians
Now we plug the values into the area formula:
Area = ((π/3)/360°) * π * 10^2
= (π/3)*(1/360)*(π)*(10)^2
= π^2/1080 * 100
≈ 9.24 cm^2
Therefore, the area of the sector OAB is approximately 9.24 cm^2.