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CHAPTER VII.

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Quantities of Materials (Cont'd).

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II. Volumes from Original Contours.

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3. Contents and Areas of Reservoirs.

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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 (A_{0} + 2 A_{1}
+ A_{2} + 2 A_{3} + .... + 2 A_{n–1} + A_{n}
– (A_{0} + A_{n}) ÷ 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.