Question

A spray irrigation system waters a section of a farmer's field. If the water shoots a distance of 85 feet, what is the area that is watered as the sprinkler rotates through an angle of 60 degrees? Use 3.14 for pi . Round your answer to the nearest square foot, and enter the number only.

Answer 1

Answer:

The watered area is approximately 3783 square feet.

Step-by-step explanation:

The area that is watered due to the rotation of the spankler is a circular section area ($A$), whose formula is:

$A = \frac{\theta }{2}\times \frac{1}{360^{\circ}}\times 2\pi \times d^{2}$

Where:

$d$ - Water distance, measured in feet.

$\theta$ - Rotation angle, measured in sexagesimal degrees.

Given that $d = 85\,ft$ and $\theta = 60^{\circ}$, the watered area is:

$A = \frac{60^{\circ}}{2} \times \frac{1}{360^{\circ}}\times 2\pi \times (85\,ft)^{2}$

$A \approx 3783\,ft^{2}$

The watered area is approximately 3783 square feet.