Design of a Semi-Circular Hopper

by Jessica Arce

Submitted : Spring 2011

For this project, I needed to find the dimensions of a half-cylinder that would minimize the cost of the hopper. In order to solve the problem, I used the equation for the volume of a cylinder as well as the equation for the surface area of a cylinder and manipulated them in order to find my results. I divided the equations by two because the problem used a half-cylinder. I then found the derivative of the equation for the surface area and solved for r. I then used r to find L and D, which were my results. The conclusion that I drew from my results is that in order to minimize the cost of the hopper, the length has to be smaller than the diameter.

[ Back ]