Cylindrical Pipe Optimization

by Yassin Eddekkaki

Submitted : Spring 2022

Mathematical descriptions can be found in multiple problems that arise from complications towards a real-world application. With regards to critical lessons in calculus teachings, optimization is defined by its ability to be among the most effective foundations of maximizing a situation or resource. It is considered a highly dependable tool in assessing the best total outcome from any situation that involves multiple variables of discrepancy. As apart of a personal endeavor, optimization has its highest value when dealing with valued resources needed for the creation of new products. In application of these concepts, this report intends to discover the optimal amount of sheet metal needed to create a pipe with a volume of 76〖in〗^3. By implementing objective equations for the volume of a metal pipe, the optimal size of the metal sheet can be found with precise accuracy with regards to money spent vs. resources actually used. By utilizing the volume of the pipe, the dimensions of the cylinder must be found in order to create an objective equation that will give us the total surface area needed to create the given material. The following step is to simplify the equation into one variable and differentiate it in order to solve for the radius. By finding the radius, the height of the pipe can be determined which will ultimately give us the correct dimensions for the metal needed to create the overall cylinder. The results of this investigation will be used to determine the surface area and optimal price for the material needed to create a necessary pipe for a home.

[ Back ]