What is the area of sector BEC when CE = 9 yd?

Solution:

The arc S is given by the relation below:

S = rC

Where r is the radius of the circle and

θ = angle subtended by the arc at the centre

In the given problem the radius CE is 9 yards

∠BEC = 120°

The arc(BC) = rθ

r = 9 yards

θ = 120° = 2.05 radians (upto two decimal places)

Hence the arc(BC) = 2.05(9) = 18.45 yards

Area of the sector BEC

= θ/360 × π × r²

= 120/360 × π × 9²

= 1/ 3  × π × 81

= 27 π

= 84.82 yard²

Area of the sector BEC is = 18.45 × 9 = 84.82 yard²

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What is the area of sector BEC when CE = 9 yd?

Summary:

The area of sector BEC when CE = 9 yd is 84.82 yard²