Answer:
Area of the sector ≈ 1496m²(nearest whole number)
Step-by-step explanation:
The sprinkler system on the farm can only rotate 140° . The rotation is not a full circle .The full angle formed for a circle should be 360°.The sprinkler spray water up to 35 meters. This is the radius of the sector formed. The area of the region that can be sprayed is the area of the sector formed with the angle 140°.
Area of a sector = ∅/360 × πr²
where
∅ = 140°
r = 35 meters
Area of a sector = ∅/360 × πr²
Area of a sector = 140/360 × π35²
Area of a sector = 140/360 × 1225π
Area of a sector = 171500π/360
Area of a sector = 476.388888889 π
Area of a sector = 476.388888889 × 3.14
Area of the sector = 1495.86111111
Area of the sector ≈ 1496m²(nearest whole number)
