"Published in Vacaville, California, USA"
A channel whose cross section is a semicircle with rise of 1 ft. per 1000 ft., is flowing full. The diameter of the channel is 6.55 ft. The vertical plane which contains the axis is perpendicular to the two vertical planes which contain the ends of the channel. If the end planes are 2000 ft. apart, find the amount of water in the channel.
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 the channel which is a right semicircular cylinder by similar triangles as follows
By Pythagorean Theorem, the length of the channel is
Therefore, the amount of water in the channel which is a right semicircular cylinder is
