Question

A water sprinkler sprays water over a distance of 36 feet while rotating through an angle of 140 degrees. What area of lawn receives​ water?

Answer 1

Answer: $1,583.36\ ft^2$

Step-by-step explanation:

The formula for calculate the area of a Sector of a circle is:

$A=\pi r^2(\frac{C}{360})$

Where "C" is the central angle in degrees and "r" is the radius.

Based on the data given in the exercise, you can identify that:

$r=36\ ft\\C=140\°$

(See the figure attached)

Then, you can substitute these values into the formula and then evaluate, in order to calculate the area of lawn that receives​ water.

The result is:

$A=\pi r^2(\frac{C}{360})\\\\A=\pi (36\ ft)^2(\frac{140\°}{360})\\\\A=1,583.36\ ft^2$