Question

A sprinkler sprays water at a distance of 32 feet. It rotates through an angle of 106°. What is the area of grass that receives water?

Answer 1

Answer:
`(13568)/(45) \pi ft^2`

Explanation:

This is basically just a circular sector problem.

the radius of our "circle" is 32 feet.

so the area of such a circle, would be
`\pi 32^2` = 1024 pi square feet.

However, the sprayer only rotates 106 degrees, and not a full 360 needed to make a circle. No problem! since 106 is 106/360th of the circle, we just take that fraction of the area:

106/360 x 1024, which is 13568/45 pi square feet, (about 301.5pi ft^2)