Question

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

Explanation:

Step1: Recall the formula for the area of a sector

The area of a sector of a circle is given by \( A=\frac{\theta}{360^{\circ}}\times\pi r^{2} \), where \( \theta \) is the central angle in degrees and \( r \) is the radius of the circle.
Here, \( \theta = 85^{\circ} \) and \( r = 5 \) meters, and \( \pi=3.14 \).

Step2: Substitute the values into the formula

First, calculate \( r^{2} \): \( r^{2}=5^{2} = 25 \).
Then, calculate \( \pi r^{2} \): \( 3.14\times25=78.5 \).
Next, calculate the fraction \( \frac{\theta}{360^{\circ}}=\frac{85^{\circ}}{360^{\circ}}\approx0.2361 \).
Now, find the area of the sector: \( A = 0.2361\times78.5 \).

Step3: Perform the multiplication

\( 0.2361\times78.5 = 0.2361\times(70 + 8.5)=0.2361\times70+0.2361\times8.5 = 16.527+2.00685 = 18.53385\approx18.5 \) (rounded to one decimal place).

Answer:

C. 18.5 square meters