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Friday, February 27, 2015

Trapezoid Prism Problems, 8

Category: Solid Geometry

"Published in Newark, California, USA"

The figure shows a right section of a railroad cut in a hillside. If the sides rise 1 unit vertically to a horizontal distance of 1.5 units, and if the length of the cut is 100 ft., find the volume of earth removed.

Photo by Math Principles in Everyday Life

Solution:

The cross section of a railroad cut in a hillside is a general quadrilateral. If you draw vertical lines from the top ends of a general quadrilateral to the bottom horizontal line that contains one side, then it becomes a trapezoid as follows

Photo by Math Principles in Everyday Life

By similar triangles, we can solve for the values of a and b as follows





The area of a trapezoid is





The area of small triangle is




The area of big triangle is




Hence, the area of the base which is the cross section of a railroad cut in a hillside is




Therefore, the volume of earth removed which is the volume of a prism is