Question

The diagram shows the areas of a lawn covered

by two water sprinklers. Which sprinkler covers
a greater area of the lawn? How much more?
45 ft
80°
Sprinkler A
40 ft
100%
Sprinkler B

Answer 1

Answer: Sprinkler A covers an area of 45 ft with an 80° angle, while Sprinkler B covers an area of 40 ft with a 100% angle.

To compare the two, we need to calculate the area covered by each sprinkler. We can use the formula for the area of a sector of a circle to do this.

For Sprinkler A:

Area = (80/360) x pi x (45/2)^2 = 795.77 sq. ft.

For Sprinkler B:

Area = (100/100) x pi x (40/2)^2 = 1256.64 sq. ft.

Therefore, Sprinkler B covers more area than Sprinkler A by approximately 460.87 sq. ft.