11.1: Examples

Let’s start with a simple question:

Example \(\PageIndex{1}\)

The diameter of a circle is?

1. One-half the radius
2. Twice the radius
3. Twice the circumference
4. One-half the circumference
5. Both b and d

Solution

Upon first examination, the answer appears to be rather obvious. It is “b”, twice the radius. However, whenever a multiple choice question uses an answer such as “e”, both a and b, you need to take a deeper look. In order to rule out answers, you need to have a good understanding of the question.

1. One-half the radius – this one should be fairly easy to rule out since you know that twice the radius is the answer.

2. Twice the radius – the correct answer

3. Twice the circumference

4. One-half the circumference

Both of these answers require you to know the formula for circumference to make an educated guess as to whether or not either of these are correct.

\[\text { Circumference }=\pi \times \mathrm{D} \nonumber \]

Knowing this equation allows you to easily rule out both of these possible answers.

This was a fairly easy example. Now let’s take a look at something a little more deceiving and requires additional work to solve.

Example \(\PageIndex{2}\)

One acre-foot of water contains?

1. 43,560 cubic feet
2. 325,829 gallons
3. 1,233,263 liters
4. Only a and b
5. All of the above

Solution

Upon first glance, most of you might say “b” is the correct answer. You would be correct, because one acre-foot does contain 325,829 gallons. However, there is a better answer.

If your next instinct tells you “d” is correct, then you would also be right. Remember, one acre of land is equal to 43,560 square feet. If you fill this land one foot deep, then it becomes 43,560 cubic feet. Therefore, both “a” and “b” are correct answers.

However, 1,233,263 liters is a large number and it might actually be equivalent to one acre-foot. Here is where you need to know how many liters are in a gallon.

1 gallon = 3.785 liters

Therefore, \(325,829 \text { gal } \times 3.785 \mathrm{L}=1,233,262.7 \mathrm{L}\)

So, the best answer is “e” all of the above.

Meter reading is a common task for both water distribution and treatment operators. Mechanical equipment such as, meters, pumps and motors require maintenance and have a certain operating life. In addition, knowing how much water a utility pumps and sells is critical to a utilities revenue stream. There are flow meters and hour meters at various facilities in a water system. Understanding some of the terminology is critical to understanding how to solve some very basic math problems.

Example \(\PageIndex{3}\)

A water treatment operator had a start read of a certain pump on January 1 and an end read on January 31. If the start read was 1,200,425 gallons and the end read was 6,342,076 gallons how much water flowed through this pump?

1. 5,142 gallons
2. 51,416 gallons
3. 5,141,651 gallons
4. None of the above

Solution

This is a relatively simple subtraction problem but you need to know what “start” and “end” reads are. Flow meters can be read daily, weekly, monthly, etc. A “start” read is nothing more than the beginning read of a certain period. In this example a monthly read. The “end” is then the last read of a certain period. So in this example, letter “c” is the correct answer, 5,141,651 gallons flowed through this pump in the month of January. Do you notice anything else interesting with this question? All the answers have similar numbers, just an order of magnitude different. The certification exams often do this to try and confuse test takers. Sometimes people get confused and might see a comma as a decimal and will select the incorrect answer.

These are only a few examples of some very basic problems and some test taking tips when you finally begin taking operator certification exams. Below are a series of questions to further illustrate the subtle differences in ways of asking questions.

Exercise 11.1

1. How many gallons of water are in 2 acre-feet?
   1. 43,560
   2. 87,120
   3. 325,829
   4. 651,658
   5. Both b and d
2. A customer used 25 CCF in February and the ending read was 8052 CCF. If the ending reading in March was 8080 CCF, how many CCF did they use in March?
   1. 25 CCF
   2. 28 CCF
   3. Not enough information to solve
   4. None of the above

3. A pressure gauge reads 100 psi. This is equivalent to

   1. 43.3 feet
   2. 110 psig
   3. 2.31 feet
   4. 231 feet
   5. 231 psig
4. The volume of cylinder is calculated by multiplying its height by
   1. 3.14
   2. 3.14 x the radius
   3. 0.785
   4. 0.785 x the diameter
   5. 0.785 x the diameter squared
5. At the beginning of the day, a totalizer on a pump station effluent meter reads 2,813,572 gallons. The next morning, the totalizer reads 4,612,931 gallons. The average daily flow during this 24-hour period was approximately
   1. 0.18 MGD
   2. 1.8 MGD
   3. 18 MGD
   4. 180 MGD
   5. 1,800 MGD
6. The past three year-end hour meter readings for a booster pump are 1152.1, 4433.3, and 7542.4. What is the greatest number of hours that the pump operated in a single year in this period?
   1. 7542.4 hours
   2. 6390.3 hours
   3. 3281.2 hours
   4. 3109.1 hours
7. A meter indicates 20 hundred-cubic feet (ccf) of water was delivered during a billing period. This is approximately
   1. 1,000 gallons
   2. 1,500 gallons
   3. 10,000 gallons
   4. 15,000 gallons
   5. None of the above
8. You are to excavate a pipe trench that is 300-feet in length, 6-feet deep, and 3-feet wide, and export all of the soil removed. Your dump truck holds 10 yards. How many trips will your truck need to make to complete the job?
   1. 5
   2. 10
   3. 15
   4. 20
   5. 25
9. A flow meter indicates a flow rate of 1,500 gallons per minute. How much water per day will flow through the meter in 110 hours?
   1. 132,353 cf
   2. 1,323,529 cf
   3. 990,000 gal
   4. 9,900,000 gal
   5. Both b and d