3650.11 – Peanut Butter Pricing

Pricing ought to be by the volume of peanut butter inside. The volume of a cylinder of radius $r$ and height $h$ is $\pi r^2 h$. For the two cans in the problem we have volumes of $\pi (1.5)^2 4 = 9 \pi$  and $\pi (3)^2 6 = 54 \pi$ respectively.

In case the answer isn't jumping right off the page, we use a proportion,

$$\begin{aligned}\dfrac{9 \pi}{54 \pi} &= \dfrac{2}{x} \\9x &= 108 \\x &= \$12.00\end{aligned}$$

Question to ponder: The solution begins with the statement that the cost should depend on the volume inside the jar.  But shouldn't the amount of material in the jar itself--the glass or plastic--be taken into account somehow too?