Chapter 12.6, Problem 22IP

To determine

To find : Minimum and maximum volume of a fire hose.

Answer to Problem 22IP

Minimum volume = $0.61{\text{ft}}^3$ and maximum volume = $9.82{\text{ft}}^3$

Explanation of Solution

Given information :

We know that minimum diameter = $1.5\text{ in}\text{.}$ and maximum diameter = $6$ in.

Height of hoses = $50$ feet.

As $1$ in = $\frac{1}{12}$ ft.

So, minimum radius = $0.0625$ feet

And maximum radius = $0.25$ feet

Formula Used:

Volume of cylinder = $\pi r^{2}h$

Calculation :

Minimum volume of hoses = $\frac{22}{7}{(0.625)}^2\times 50$

  $=0.6138{\text{ ft}}^{\text{3}}=0.61{\text{ft}}^3$

Maximum volume of fire hoses

  $\begin{array}{l}$ =(3.14){(0.25)}^2\times 50$=9.8214{\text{ ft}}^{\text{3}}\end{array}$