Chapter 12.5, Problem 15WE

To determine

To find: Thebest ball to buy.

Answer to Problem 15WE

The large ball is better to buy.

Explanation of Solution

Given information:

The string is sold in a ball $6\text{cm}$ in a diameter and in a ball $6\text{cm}$ in a diameter.

Calculation:

Volume of ball is proportional to the cube of diameter.

  $\begin{array}{c}\frac{\text{Volume}\text{of}\text{larger}\text{ball}}{\text{Volume}\text{of}\text{smaller}\text{ball}}={\left(\frac{12}{6}\right)}^3\\ \frac{\text{Volume}\text{of}\text{larger}\text{ball}}{\text{Volume}\text{of}\text{smaller}\text{ball}}={\left(\frac{2}{1}\right)}^3\\ \frac{\text{Volume}\text{of}\text{larger}\text{ball}}{\text{Volume}\text{of}\text{smaller}\text{ball}}=\frac{8}{1}\end{array}$

Calculate the price per unit volume for smaller ball.

  $R_1=\frac{1}{V_1}$

Calculate the price per unit volume for larger ball.

  $R_2=\frac{\$6.5}{V_2}$

Calculate the ratio of prices.

  $\begin{array}{c}\frac{R_1}{R_2}=\frac{\left(\frac{1}{V_1}\right)}{\left(\frac{6.5}{V_2}\right)}\\ =\left(\frac{V_2}{V_1}\right)\left(\frac{1}{6.5}\right)\\ =\frac{8}{6.5}\\ =1.23\end{array}$

Since, $\frac{R_1}{R_2}>1$ hence large ball is better to buy.

Therefore,thelarge ball is better to buy.