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Solutions to I-Practice Math #4

22. You need to control an algae bloom in your 20,000,000 gallon raw water reservoir.  The herbicide directions recommend applying 25 pounds/acre.  If the average depth of the reservoir is 15 feet and each bag contains 40 pounds of herbicide, you need ____ bags.

 20,000,000 gal ¸ 7.48 gal/ft³ = 2,673,797 ft³

 2,673,797 ft³ ¸ 15 ft = 178,253 ft²

 178,253 ft² ¸ 43,560 ft/acre = 4.09 acres

 4.09 acres x 25 lbs/acre = 102.3 lbs

 102.3 lbs ¸ 40 lbs/bag = 2.56 bags

 Need 3 bags

23.  To dose a flow of 0.6 mgd at 1.8 mg/L, you need ____ 40 pound bags of the chemical.

 0.6 mgd x 1.8 mg/L x 8.34 lbs/gal = 9 lbs/day

 Need 1 bag

24.  You try to maintain a 120 day supply of all chemicals.  If a bag contains 40 pounds of chemical, how many bags of a chemical are needed to dose a flow of 0.6 mgd at 1.8 mg/L?

 0.6 mgd x 1.8 mg/L x 8.34 lbs/gal = 9 lbs/day

 9 lbs/day x 120 days = 1,080 lbs

 1,080 lbs ¸ 40 lbs/bag = 27 bags

25.  The hopper for your chemical feeder is conical in shape with a reserve tank on top.  The hopper has a diameter of 12 feet and a depth of 8 feet.  The reserve tank is 20 feet high.  The total volume of the hopper and the reserve tank is _______ ft³.

 Hopper:  12 ft x 12 ft x 0.785 x 8 ft ¸ 3 = 301 ft³

 Reserve:  12 ft x 12 ft x 0.785 x 20 ft = 2,260 ft³

 Total:  301 ft³ + 2,260 ft³ = 2,561 ft³

26.  The hopper for your chemical feeder is conical in shape.  If it has a diameter of 12 feet and a depth of 8 feet, the volume of the hopper is _______ ft³.

 12 ft x 12 ft x 0.785 x 8 ft ¸ 3 = 301 ft³

27.   Calculate the molecular weight of H₂CO₃.  The atomic weight of calcium is 40, oxygen is 16, carbon is 12, and hydrogen is 1.

 2 x 1 + 1 x 12 + 3 x 16 = 62

28.   Calculate the molecular weight of H₂O.  The atomic weight of calcium is 40, oxygen is 16, carbon is 12, and hydrogen is 1.

 2 x 1 + 1 x 16 = 18

29.  Calculate the molecular weight of Ca(HCO₃)₂.  The atomic weight of calcium is 40, oxygen is 16, carbon is 12, and hydrogen is 1.

 1 x 40 + 2 x 1 + 2 x 12 + 6 x 16 = 162

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