3650.11 – Peanut Butter Pricing

Tags:Problem Set 12Pre-AlgebraGeometry-Euclidean

If a glass jar of all natural peanut butter 3 inches in diameter and 4 inches tall sells for $2.00, what is a fair price for one that is 6 inches in diameter and 6 inches tall?


Pricing ought to be by the volume of peanut butter inside. The volume of a cylinder of radius rr and height hh is πr2h \pi r^2 h. For the two cans in the problem we have volumes of

π(1.5)24=9π\pi (1.5)^2 4 = 9 \pi


π(3)26=54π\pi (3)^2 6 = 54 \pi

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

9π54π=2x\frac{9 \pi}{54 \pi} = \frac{2}{x} 9x=1089 x = 108 x=$12.00.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?