A water sprinkler has a range of 5 meters as shown.

Question

The jet of water from the sprinkler sweeps out at an angle of 85° as the nozzle turns. What is the area watered by the sprinkler? Use the value π = 3.14, and round your answer to one decimal place.

A. 

15.6 square meters

B. 

17.8 square meters

C. 

18.5 square meters

D. 

19.2 square meters

Answer 1

It's sector time!

Recall the formula for the area of a sector of a circle if given radians: A = (1/2)r²θ

You may have also seen this formula for the case when given degrees: A = (n°/360°)πr²

Let's try both!

RADIANS

85 degrees in radians is equal to (85°)(π/180) = 17π/36 radians. Radius r = 5 meters, and π ≈ 3.14.

A = (1/2)r²θ

A = (1/2)(5)²(17π/36)

A = 18.5 square meters, which corresponds to choice C.

DEGREES

Use the same facts as earlier, but keep the sector angle measurement as 85°.

A = (n°/360°)πr²

A = (85/360)π(5)²

A = 18.5 square meters, which corresponds to choice C.