An engineer is asked to design a water sprinkler that will cover a field of 100 square yards that is in the shape of a sector of a circle of radius 50 yards. Through what angle should the sprinkler rotate?
Hello, magentarita!
An engineer is asked to design a water sprinkler that will cover a field
of 100 square yards that is in the shape of a sector of a circle of radius 50 yards.
Through what angle should the sprinkler rotate?
We are expected to know the area formula for a sector of a circle: . .[1]
. . where is the radius and is the central angle in radians.
We know: .
Substitute into [1]: .
Therefore: .