Chapter 9.2, Problem 27E

To determine

To find: The length of the safety rail and the area of the deck.

Answer to Problem 27E

The length of the safety rail is $15.7\text{yd}$ and the area of the sector is $78.5\text{yd}$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

Consider the given diagram and convert the radian measure into the degree measure.

The radian measure of the angle $90°$ is $\frac{\pi }{2}$ radians.

Then, the arc length is obtained as,

  $\begin{array}{r}S=10\left(\frac{\pi }{2}\right)\\ =15.7\text{yd}\end{array}$

The area of the sector is obtained as,

  $\begin{array}{c}A=\frac{1}{2}\left(10\right)\left(10\right)\frac{\pi }{2}\\ =78.5{\text{yd}}^2\end{array}$

Thus, the length of the safety rail is $15.7\text{yd}$ and the area of the sector is $78.5\text{yd}$ .