Chapter 9.4, Problem 41E

To determine

To calculate the area of the ground being watered.

Answer to Problem 41E

The area of the ground being watered is approximately 20.42 square feet.

Explanation of Solution

Given information:

The sprinkler is set to rotate $65°$ and spray a distance of 6 feet.

Formula used:

Area of a circular sector $A=\frac{1}{2}\pi r^2\theta$

Calculation:

First convert angle in radian

  $\begin{array}{l}65°=65\cdot \frac{\pi }{180}\\ =\frac{13}{36}\pi \end{array}$

Area of the ground being watered

  $\begin{array}{l}=\frac{1}{2}\pi r^2\theta \\ =\frac{1}{2}\pi 6^2\cdot \frac{13}{36}\pi \left[\text{radius is 6 feet}\right]\\ \approx 20.42\end{array}$

The area of the ground being watered is approximately 20.42 square feet.