A water sprinkler sprays water over a distance of 50 feet wh

A water sprinkler sprays water over a distance of 50 feet while rotating through an angle of 130 degree. What area of lawn receives water?

Solution

Assume the lawn is a circle with radius r = 50 ft.

we know Area of circle = ( pi) r^2

Area of the whole circle = (pi)*50^2 sq.ft.

Proportion:

x / (pi)*50^2= 130/360

x / 2500(pi) = 13 / 36

x = ( 13 / 36 ) 2500( pi )

x = ( 0.361111111) ( 2500( pi) )

x = 8125( pi) / 9

x = 2836.16003 sq.ft.