A correspondent writes and asks us the above question, and as it is one of general interest to machinists, we give a diagram to illustrate our answer :— Make the line, A B, in the accompanying diagram equal to the diameter of the base of the drum, and C D equal to the diameter of the smaller end of the cone ; draw the lines, A C and B D, and prolong these lines until they meet at the point, E, strike two arcs, D F and B G, the first with E D, and the second with EB for radius, make the arc, D F, equal to the circumference of the smaller end, and B G equal to the circumference of the base of the cone, draw the line, F G, which will pass through the point, E, and the piece D B G F, if cut out. will exactly cover the cone drum. In order to find the lengths of the arcs. D F and B G, it is only necessary to know the angle, D E F, which will correspond to these arcs, and the number of degrees of this angle can be found by multiplying 360 with the length of one half of the line, C D, taken in inches, and dividing the product by the length of the line, D E.
How to Cut a Piece of Leather which will Exactly fit a Cone Drum
This article was originally published with the title "How to Cut a Piece of Leather which will Exactly fit a Cone Drum" in Scientific American 13, 36, 286 (May 1858)