"Published in Vacaville, California, USA"
The outer protective smokestack of a steamship is streamlined so that it has a uniform oval section parallel to the deck. The area of this oval section is 48 sq. ft. If the length of the stack is 18 ft. and if the axis is raked 76°15' to the horizontal, find the volume enclosed by the stack. (Raked means inclined.)
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 area of a base which is an oval section is already given in the problem. By using a trigonometric function of a right triangle, the altitude of the smokestack is
Therefore, the volume of a smokestack which is a cylinder is
