2.2: Applying the Math of Geometric Shapes
 Page ID
 7129
As with all mathematical computations, there is an element of “Will I ever use this outside of the classroom?”. The answer is most likely “sometimes.” An operator might calculate the volume of water in a storage structure or pipeline to determine how much chlorine is needed to disinfect the structure. A contractor might calculate the internal surface area of a tank to determine the amount of coating that is required. Or, you might be asked to paint the interior walls of a room. Putting practical use to mathematical equations can help in the student’s overall understanding. The following problems are some “realworld examples” you might find working as a water utility operator.
Exercises

A water utility operator needs to determine how many gallons of paint are needed to paint the outside of an aboveground storage tank and the cost of the paint. The tank has a 120foot diameter and is 32 feet tall. (Assume that one gallon of paint can cover 125 ft^{2} and costs $25.75 per gallon)

A utility manager needs to find a site for a 3.1 MG storage tank. The tank cannot be taller than 33 feet. What diameter should this tank have?

A construction crew will be installing 1,250 feet of 10inch diameter pipe. The width of the trench will be 30 inches and the depth 36 inches. After the pipe has been installed, how many cubic yards of dirt will be needed to backfill the trench? (Assume the trench will be backfilled up to 6 inches from the ground surface)

In the above problem, the construction crew also needs to place 6 inches of aggregate base on top of the fill. How many cubic feet of base are needed?

A water quality technician needs to disinfect an elevated storage tank, but first, she needs to calculate the volume of water in the tank. The 20foot diameter storage tank sits on a 16foot diameter, 30foot tall pipe. How many gallons are in the structure?

A private contractor needs water for a grading project. In a similarsized job, he used 155 tank loads from a water tower. The tower is shaped like a “pill.” Each end has a 15foot diameter and the center section is 30 feet long. If the water costs $425 an acrefoot, how much does the contractor need to budget for water?

A maintenance crew is replacing a 12” meter at a well. The specifications state that there needs to be 3 times the pipe diameter in feet of straight pipe before the meter and 5 times the pipe diameter in feet of straight pipe after the meter. Currently, the well has a 10” diameter pipe. How many feet of 12” pipe are needed?

A 1.25mile section of trapezoidal shaped aqueduct needs to be drained. The aqueduct is 5 feet wide at the base and 10 feet wide at the water line. If there are 9 acrefeet of water in the aqueduct, what is the depth?

A contractor just installed 350 feet of 8” diameter pipe, 430 feet of 12” diameter pipe, and 275 feet of 16” diameter pipe. The pipe needs to be filled, but the inflow flow rate is only 10 gpm. How long will it take to fill all this pipe? (Give answer in the best time format)

A water utility manager is determining what shaped storage tank should be used to store water for a small mobile home park. The mobile home park needs 110,000 gallons of storage. There is room for a 25foot diameter and 30foot tall cylindershaped tank or a 30foot diameter sphereshaped tank. Which tank will provide the adequate storage?

In the problem above, how much shorter expressed as a percentage is the smaller tank?