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Tuesday, August 12, 2014

Triangular Prism Problems, 3

Category: Solid Geometry

"Published in Newark, California, USA"

A trough is formed by nailing together, edge to edge, two boards 11 ft. in length, so that the right section is a right triangle. If 15 gals. of water are poured into the trough and if the trough is held level so that a right section of the water is an isosceles right triangle, how deep is the water? (231 cu. in. = 1 gal.)

Photo by Math Principles in Everyday Life

Solution:

Consider the cross section of a trough which is the base of a triangular prism

Photo by Math Principles in Everyday Life

The cross section area of water in a trough is




The length of a trough in inches is




The volume of water in a trough in cubic inches is




Therefore, the height or deep of water in a trough is