## Quantities of Materials (Cont'd).

### Application of Prismoidal Formula.

The formula previously demonstrated for finding the volume of any number of continuous prismoids of the form under discussion and given on Pg. 76 of this Chapter is
V cu. ft. = (L × 2) ÷ 3 (A0 + 2 A1 + A2 + 2 A3 + .... + 2 An–1 + An – (A0 + An) ÷ 2) ... (19)
or
V = (L × 2) ÷ 3 (Sum Even A's + 2 Sum Odd A's – ½ Sum Extreme A's) ... (20)

in which V was the total volume in Cu. Ft. of the n continuous prismoids and n is an even number. Since the vertical distance between the contours in one ft.

L = 1 in. Eq.19 and since 1 U. S. Gallon = .13368 Cu. Feet by substituting these values in Eq. 19 we have

V = (1 × 2) ÷ (3 × .13368) (Sum Even A's + 2 Sum Odd A's – ½ Sum Extreme A's) ... (21)
or by reduction the Vol. in U. S. Gallons is
V = 4.987 (Sum Even A's + 2 Sum Odd A's – ½ Sum Extreme A's) ... (22)
which is the general equation required.

Since the given diagram has been plotted to a scale of 1 inch = 20 ft., 1 Sq. inch = 400 Sq. ft. and including this in the general formula we have as the Equation of this particular case (since 4.987 × 400 = 1994.8)

V = 1994.8 (Sum Even A's + 2 Sum Odd A's – ½ Sum Extreme A's) ... (22)
the required volume being expressed in U. S. Gallons.