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Wednesday, December 12, 2012

More Right Circular Cylinder Problem

Category: Solid Geometry, Trigonometry

"Published in Newark, California, USA"

At what angle with the horizontal must the base of a right circular cylinder be tilted to make it just topple over if its diameter is 12 ft. and its altitude is 16 ft.? (The center of gravity is at the middle point C of the axis of the cylinder. The base must be tilted so that the line AC becomes vertical.)

Photo by Math Principles in Everyday Life


By looking at the figure, we need to analyze the small triangle because we want to get the angle of tilt for right circular cylinder. Consider the figure below

Since the triangle is a right triangle, we can use the basic trigonometric function to solve for angle θ and ϕ as follows

Therefore, we can get the angle of tilt as follows

                                     θ + ϕ = 90º 

                           53.130º + ϕ = 90º

                                           ϕ = 90º - 53.130º

                                           ϕ = 36.870º