Mensuration for sheet metal workers, as applied in working ordinary problems in shop practice by Neubecker William b. 1864

Author:Neubecker, William, b. 1864
Language: eng
Format: epub, pdf
Tags: Sheet-metal work
Publisher: New York, D. Williams Company
Published: 1907-03-25T05:00:00+00:00

the lower base of which is 20 inches, the upper base 10 inches,

and a section taken midway between the two —

or 15 inches, as a b. To obtain the area of these planes multiply the square of one of the sides of the regular poly-

1,1,064,022.2208 ou. in.

4,006 gallons and 5 gills

Fig. 40.—Contents of Frustum of Cone.

gon by the multiplier giyen in the following table for the proper polygon:

Name. Sides to polygon. Multiplier.

Triangle 3 0.433

Square 4 1.000

I'entagon 5 1.720

Hexagon 6 2..598

Heptagon 7 3.634

Octagon 8 4.828

Nonagon 9 6.182

Decagon 10 7.694

As the shape in question is a hexagon, we find the

multiplier in the table to be 2.598. Then, following the

above rule, the area of the lower plane is equal to 20 X 20

==400; 400X2.598^1039.2. The area of the upper

plane, 10 X 10 X 2.598 = 259.8, and four times the area

of the middle plane, 15 X 15 X 2.598 X 4 = 2338.2.

24 Theii 1039.2 + 259.8 -f 2338.2 = 3637.2. 3637.2 X ^ =

14,548.8 cubic inches contents. This divided by 231 = 63 gallons, or 2 barrels, less 4.2 cubic inches.

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