"Published in Newark, California, USA"
A railway cut 200 ft. and 30 ft. wide at the bottom is made with sloping sides, which are 80 ft. and 60 ft. in length. The 80 ft. side is inclined 45° and and the other side is inclined 30° to the horizontal. Find the cost of removing the earth at $2 per load, if the trucks have a capacity of 4 cu. yd.
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| Photo by Math Principles in Everyday Life |
Solution:
Consider the given figure above
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| Photo by Math Principles in Everyday Life |
To understand more the problem, it is better to analyze the front side which is a quadrilateral and the base of the prism, and then label further as follows
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| Photo by Math Principles in Everyday Life |
If you draw vertical lines from the two upper vertices and horizontal lines from the two lower vertices of a quadrilateral, then it becomes a trapezoid. Since the sides and angles of a quadrilateral are given, then we can solve the remaining sides of two right triangles.
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| Photo by Math Principles in Everyday Life |
The area of a trapezoid is
The area of 45° right triangle is
The area of 30° right triangle is
The area of a quadrilateral which is the base of a prism is
The volume of the earth removed from a railway cut which is the volume of a prism is
The volume of a prism in cubic yards is
Therefore, the cost of removing the earth from a railway cut is
