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,

$\frac{9 \pi}{54 \pi} = \frac{2}{x}$ $9 x = 108$ $x = \$12.00.$

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?