"Published in Vacaville, California, USA"
A smokestack of a ship is 25 ft. long with a rake aft (angle of the stack's inclination from the vertical) so that its top rises 24 ft. above the deck. The cross section of the flue is a circle with a diameter of 3½ ft. Completely encircling the flue is a protective stack. The distance between the two stacks is 6 in. Find the space enclosed between the two stacks and also the outside painting surface of the protective stack. (Neglect the thickness of the metal).
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| Photo by Math Principles in Everyday Life |
Solution:
Consider the given figure above
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| Photo by Math Principles in Everyday Life |
The cross section of a smokestack of a ship is a two concentric circles. The area of the region between the two concentric circles is
Therefore, the amount of space enclosed between the two stacks of a smokestack which is the volume of a circular cylinder is
and the amount of outside painting the surface of a smokestack is
