Chapter 7.3, Problem 35E

(a)

To determine

To Find: The expression for the efficiency ratio $\frac{S}{V}$ of the cylinder

Answer to Problem 35E

  $\frac{S}{V}=\frac{2(h+r)}{rh}$

Explanation of Solution

Given: You are giving three cylindrical containers.

Given: $\frac{S}{V}$

Where $S$ be the surface area of the cylinder and $V$ be the volume of the cylinder.

Then

  $\frac{S}{V}=\frac{2\pi rh+2\pi r^2}{r^{2}h}=\frac{2(h+r)}{rh}$

Hence, $\frac{S}{V}=\frac{2(h+r)}{rh}$

(b)

To determine

To Find: The efficiency ratio $\frac{S}{V}$ of each cylindrical can listed in the table. Rank the three cans according to the efficiency.

Answer to Problem 35E

  $0.78,0.38,0.34$

Explanation of Solution

Given:

  

Given: $\frac{S}{V}$

Where $S$ be the surface area of the cylinder and $V$ be the volume of the cylinder.

Then

  $\frac{S}{V}=\frac{2\pi rh+2\pi r^2}{r^{2}h}=\frac{2(h+r)}{rh}$

  $\begin{array}{l}\frac{S}{V}=\frac{2(10.2+3.4)}{10.2(3.4)}=0.78\\ \frac{S}{V}=\frac{2(15.9+7.8)}{(15.9)(7.8)}=0.38\\ \frac{S}{V}=\frac{2(19.4+8.4)}{19.4(8.4)}=0.34\end{array}$

Hence,

The efficiencies are $0.78,0.38,0.34$