A sprinkler system on a farm rotates 140° and sprays water up to 35 meters. Find the area of the region that can be irrigated with the sprinkler.

Round your answer to the nearest whole number

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)