Calculating Volume

The three Rs (as in the letter R) are the foundations of a basic skills-orientated education program within schools: reading, writing and arithmetic. The phrase ‘the three Rs’ is used because each word in the phrase has a strong R phoneme (sound) at the beginning. The age-old fear of most people is one of the three R’s – arithmetic, better known as math. In the fields of wastewater, drinking water and solid waste treatment, there are many operators who use mathematics or its principles on a daily basis. Solving for flow rates, calculating how much sludge to waste and how often, determining how much waste is accumulating and calculating chlorine dosages are among the necessary calculations associated with operations and are routinely calculated by operators. Although these types of calculations are routinely performed, for some students entering certification class, math becomes public enemy number one. Students freeze up, draw a blank, break out in chills or hives and completely lose focus due to their strong aversion to math. The best way to tackle a fear of arithmetic is to practice. The more times one spends working math problems when preparing for a test, the more familiar and easy the problems will become. Keep in mind the old adage–practice makes perfect. I will now introduce some simple concepts that appear on the certification tests.

  • The volume of a rectangular area, such as a tank, is calculated by multiplying the length by the width by the height.
    • V = L x W x H
  • The volume of a cylinder is calculated by either multiplying π (pi) by the radius, squared times the height or .785 times the diameter, squared times the height.
    • V = π R² x H
    • V =  0.785 x D² x H
  • We measure volume in the units of either ft.3 or gallons.
  • Also, 1 ft.3 = 7.48 gallons by conversion

Now let’s try a couple practice problems. Calculate the volume of the tank in cubic feet with a length of 200 feet, width of 80 feet and a depth of 50 feet.

V = L x W x H
V = (200 ft.) (80 ft.) (50 ft.)
V = 800,000 ft.3

What is the capacity, in gallons, of an aerobic digester that is 30 feet in diameter and 47 feet tall?

V = .785 x D2 x H
V = .785 x (30 ft.)² x (47 ft.)
V = .785 x (900 ft.2) x (47 ft.)
V = .785 x (42,300 ft.3)
V = 33,205.50 ft.3
V = 33,205.50 ft.3 x 7.48 gallons per ft.3
V = 248,377.14 gallons

Check out the Test Your Knowledge – Calculating Volume post for additional practice problems.

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