1 Noy., 1902.] QUEENSLAND AGRICULTURAL JOURNAL. 377 
RULE TO FIND THE VOLUME OF A DAM WITH 
SLOPING SIDES. 
Find the area of the top and bottom. Add these areas together. Then 
find the area of a section parallel to the top and bottom and half 
way between them. Multiply this by 4, and add the result to the 
sum of the two areas found. Now multiply the total sum by the 
depth, and one-sixth of the product will be the volume of the dam. 
The answer given in the July issue of the Journal, page 64, was 
worked by this rule. (Diag. 1.) 
i Diagram (.. 
Diagram 
BS Ft 
22 Yds. 
‘yds 15 fr. 
The excavation is in the form of a frustum of a wedee. If A 
and B are the areas of the top and bottom and M the area of the 
mid-section parallel to the ends, and & the depth, then the yolume 
of the dam = a (A + B+ 4M) 
2 
Thus— A = 22 x 22 = 484 square yards 
BS 1h oy SpA 5 
M = » (22 + 11) and } (22 + 11) that is 164 yards and 163 
yards -. M=16°5 x 165 = 272-25 square yards 
4 M = 1,089 square yards. k= 4% yards 
Hence % (484 + 121 + 1,089) = 564% cubic yards. 
In the case of your dam (Diag. 2) the calculation is the same, 
substituting feet for yards ‘Thus —- 
The volume of the dam = & (A + B+4M) 
Here we have— 
A = 25 x 20 = 500 square feet 
B=15x10=150 , , 
The mid-dimensions are } (20 + 10) and 3 (25 + 15) that is 15 
feet and 0 feet. 
Therefore— 
M = 15 x 20 square feet = 300 square feet 
4 M = 1,200 square feet: 
k = 5 feet 
Hence the volume is— 
§ (500 + 150 + 1,200) cubic feet = 2 x 1,850 = 1,5412 cubic 
feet = 57:09 cubic yards 
Nors.-The depth is shown out of proportion to the scale in order to clearly define the 
middle section, 
