Math CentralQuandaries & Queries


Question from clint, a student:

the pennsylvania railroad found it necessary,owing to land slides upon the roadbed,to reduce the angle of inclination of one bank of certain railway cut near pittsburgh,pa.,from an original angle of 45 degrees to a new angle of 30 degrees. the bank as it originally stood was 200 ft.long and had a slant length of 60 ft. find the amount of the earth removed, if the top level of the bank remained unchanged.

Hi Clint,

I drew a diagram of what you described and put some labels on it.


The volume you want is the volume of the triangular prism with base the triangle ABC and height 200 feet. The volume of this region is the area of the triangular base ABC times the height of 200 feet. Finding the area of triangle ABC is an exercise with a 45-45-90 triangle and a 30-60-90 triangle. Can you see how to do it?

Write back and tell us what you did if you need more help.

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