"Published in Vacaville, California, USA"
A cylindrical tank, diameter 1 ft., length 6 ft., is placed so that its axis is horizontal. How many pounds of water will be used in filling it to a depth of 9 in., if water weighs 62.4 lb. per cu. ft.?
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 |
If a right circular cylinder whose axis is placed in a horizontal position, then its base is a circular segment. We need to get the area of its base first so that we can solve for the volume of water in a right circular cylinder. Let's analyze the cross section which is the base of a cylinder that is partially filled with water as follows
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| Photo by Math Principles in Everyday Life |
By Pythagorean Theorem, the length of AD or DB is
Since ∆AOD or ∆BOD is a right triangle, then by using trigonometric function, the value of ∠AOD or ∠BOC is
The area of circular segment ABC is
The area of the base of a cylinder filled with water is
Hence, the volume of water in a right circular cylinder is
Therefore, the weight of water in a right circular cylinder is
