A sector of a circle of radius 9cm subtends angle 120° at the centre of the circle. Find the area of the sector to the nearest cm\(^2\) [Take π = 22/7]

A sector of a circle of radius 9cm subtends angle 120° at the centre of the circle. Find the area of the sector to the nearest cm\(^2\) [Take π = 22/7]

Answer Details

To find the area of a sector, we need to use the formula:
Area of sector = (θ/360) x πr²
where θ is the angle subtended at the centre of the circle, r is the radius of the circle, and π is a mathematical constant approximately equal to 22/7.
In this case, the radius is given as 9cm and the angle is given as 120°. So, substituting these values into the formula, we get:
Area of sector = (120/360) x (22/7) x 9²
= (1/3) x (22/7) x 81
= 754/7
≈ 107.71 cm² (rounded to the nearest cm²)
Therefore, the correct answer is: 85 cm² (option C).