Chapter 7.3, Problem 36E

(a)

To determine

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

Answer to Problem 36E

  $\begin{array}{l}\frac{S_1}{V_1}=\frac{4h+2s}{sh}\\ \frac{S_2}{V_2}=\frac{4h+s}{sh}\end{array}$

Explanation of Solution

Given: A popcorn company is designing a new tin with the same square base and twice the height of the old tin.

  

Given: $\frac{S_1}{V_1}$

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

Then

  $\begin{array}{l}\frac{S_1}{V_1}=\frac{4sh+2s^2}{s^{2}h}=\frac{4h+2s}{sh}\\ \frac{S_2}{V_2}=\frac{4s(2h)+2s^2}{2s^{2}h}=\frac{4h+s}{sh}\end{array}$

Hence,

  $\begin{array}{l}\frac{S_1}{V_1}=\frac{4h+2s}{sh}\\ \frac{S_2}{V_2}=\frac{4h+s}{sh}\end{array}$

(b)

To determine

To Explain: Did the company make a good decision by creating a new tin?

Answer to Problem 36E

Bad decision

Explanation of Solution

Given: A popcorn company is designing a new tin with the same square base and twice the height of the old tin

  

Since,

  $\frac{S_1}{V_1}>\frac{S_2}{V_2}$

The company made a wrong decision.

Because the efficiency of the new tin is smaller.