88 CISTERNS. 



To find the number of gallons in tub-shaped cisterns. 



RULE. Find the cubes of the top and bottom diameters 

 in inches, by means of the table on page divide the 



difference between those cubes by the difference of the 

 diameters in inches, and multiply this quotient by .7854, 

 and again by J of the depth in inches, and divide the pro- 

 duct by 231. The quotient will be the number of gallons. 



EXAMPLE. Given, a tub-shaped cistern of a top diameter 

 of 10 feet, a bottom diameter of 8 feet, and 6 feet deep. 

 How many gallons will it contain ? 



SOLUTION. Cube of 120 inches, the top diameter, 1728000 



" 96 " " bottom " 884736 



Difference between cubes of diameters, 843264 



Divided by 24, difference of diameters, gives .35136 



Multiplied by .7854, gives 27595.8144 



" again by 24, the depth in inches, gives 662299.5456 



Divided by 231, cubic inches in a gallon, gives 2867.09 

 galls. ATM. 



RULE 2. Add the top and bottom diameters in inches 

 and divide by 2 for the mean diameter. Find the area in 

 square inches of the mean diameter by means of the table 

 on page or by the rule given on page Multiply 



the area by the depth in inches, and divide the product by 

 231, and the quotient will be the number of gallons. 



EXAMPLE. What are the contents in gallons of a cistern 

 8 feet diameter at the top, 6 feet at the bottom, and 4 feet 

 deep ? 



