Page:Sheet Metal Drafting.djvu/181

75. Related Mathematics on Short Handled Dipper.—Volume of a Frustum of a Cone of Revolution.—The frustum of a cone has a circular top and a circular base. These are known as the upper and lower bases of the frustum. The altitude of the frustum is the shortest distance between the upper and lower bases, and is always measured perpendicularly. The volume of a frustum is found by adding together the area of the upper base, the area of the lower base, and the square root of the product of the upper base area times the lower base area; the sum of these quantities is then multiplied by one-third of the altitude. Expressed as a formula

In applying this formula to Fig. 236, the areas of the upper and lower bases must first be computed.

Area of Circle	=	D2×.7854 (Chapter II)
6¼2×.7854	=	30.68 area of upper base
4½2×.7854	=	15.904 area of lower base

Known values can now be substituted in this formula

$\scriptstyle {V=(30.68+15.904+{\sqrt {30.68\times 15.904}})\times 3{\frac {3}{4}}\div 3}$

Performing the arithmetic:

$\scriptstyle {3{\frac {3}{4}}\div 3={\stackrel {\scriptstyle {~5}}{\frac {{\cancel {1}}{\cancel {5}}}{4}}}\times {\frac {1}{\cancel {3}}}=1{\frac {1}{4}}}$

15.904     30.68    127232    95424 477120 487.93472

4!√487.934722.08+ 4|√4 42|087 42|084 4408|3 9347 4408!3 5264 4408 !34083