Chapter 6.1, Problem 116AYU

(a)

To determine

To find: The length of the outfield fence.

Answer to Problem 116AYU

The length of the outfield fence is $335.1\text{ft}$ .

Explanation of Solution

Given:

The outfield is given as follows.

  

Calculation:

Calculate the angle in radian.

  $\begin{array}{c}\theta =96\times \frac{\pi }{180}\\ =\frac{8\pi }{15}\text{rad}\end{array}$

Determine the length of the outfield fence by using the arc length formula.

  $\begin{array}{c}S=r\theta \\ =200\times \frac{8\pi }{15}\\ \approx 335.1\text{ft}\end{array}$

Hence, the length of the outfield fence is $335.1\text{ft}$ .

(b)

To determine

To find: The area of the warning track.

Answer to Problem 116AYU

The area of the warning track is $3267.26{\text{ft}}^{\text{2}}$ .

Explanation of Solution

Given:

The outfield is given as follows.

  

Calculation:

Determine the area of the warning track by subtracting the area of the field without warning track from the area of the field.

  $\begin{array}{c}A=A_1-A_2\\ =\frac{\pi r_1^2\theta }{2}-\frac{\pi r_2^2\theta }{2}\\ =\frac{\left({200}^2-{190}^2\right)}{2}\times \frac{8\pi }{15}\\ =3267.26{\text{ft}}^{\text{2}}\end{array}$

Hence, the area of the warning track is $3267.26{\text{ft}}^{\text{2}}$ .