Fill Needed for a Highway Overpass

by Perla Espinoza

Submitted : Spring 2012

This project consisted of the fill needed for a highway overpass. The idea for the project was to find the volume of the fill needed to raise the highway overpass to comply with the set restraints. After identifying that the problem would require integration in order to solve for the volume, it was then needed to find what was to be integrated. Recognizing that the cross sections of the overpass were trapezoids, the formula for the area of a trapezoid was utilized and modified to use the variables that were presented with the initial problem.

After the manipulations to the area formula of a trapezoid were done, it was then integrated from 0 to L with respect to the variable x. This produced a generic formula that could be used to solve for the volume of fill needed for one side of the overpass, multiplying this formula by two would then give the total volume of the fill. Imputing the given values then gave the final answer in meters cubed.

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