"Published in Newark, California, USA"
An air duct in the form of a circular cylinder has a cross section of diameter 16 in. The distance between the bases is 20 ft., and the elements are inclined at an angle of 50° to the bases. Find the amount of magnesia required to protect the duct with a magnesia covering ½ in. thick.
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 |
Since the distance of the two bases which is the altitude and the angle of inclination of the elements with respect to the bases are given, then we can solve for the length of element which is the length of an air duct by using sine function as follows
The area of a cross section of an air duct is
Therefore, the amount of magnesia required to protect the air duct which is the volume of a circular cylinder is
