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Friday, January 16, 2015

Circular Cylinder Problems, 4

Category: Solid Geometry

"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).

Photo by Math Principles in Everyday Life

Solution: 

Consider the given figure above

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