"Published in Newark, California, USA"
A circular concrete conduit, whose inside diameter is 10 ft., is 1 ft. thick. It rises 16 ft. per 1000 horizontal feet. The vertical plane which contains the axis is perpendicular to the two vertical planes which contain the ends of the conduit. If the ends are 3000 ft. apart, find the amount of concrete used in the construction of the conduit.
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
The first thing that we need to do is to solve for the altitude or vertical distance of the ends of a conduit which is a right circular cylinder by similar triangles as follows
By Pythagorean Theorem, the length of a concrete conduit is
The cross section of a concrete conduit is a two concentric circles. The area of the region between the two concentric circles is
Therefore, the amount of a concrete used for the construction of a conduit which is the volume of a circular cylinder is
