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Firefighter Math: 3.1 Volume or Capacity

Volume is used to indicate the capacity of a tank or container. It is used by firefighters to answer questions like "How much water is left in the tank?" and "At 15 gallons per minute (gpm), how many more minutes before the tank is empty?" 

VOLUME OF A RECTANGULAR OBJECT

The volume of a rectangular container is determined by multiplying the length (l) by the width (w) by the height (h).

volume

Volume = length × width × height
V = l × w × h

Example 1 - Determine the volume of the tank in gallons.

Example 1 Image

Step 1. Use the equation for determining the volume of a rectangle. V = l × w × h

Step 2. Identify the length, width, and height. l = 5 ft, w = 6 ft, h = 8 ft

Step 3. Set up the problem and solve. V = 5ft × 6ft × 8ft = (5 × 6 × 8) (ft × ft × ft) = 240 ft3

Step 4. Determine the appropriate conversion factor. 1 cubic foot = 7.4805 gallons

Step 5. Set up the cancellation table so all units will cancel except gallons (see Section 2.1).

Cancellation Table

The volume of the tank of water is 240 cubic feet or 1,795 gallons.

Example 2 - The water tank on a newly designed engine is 34 inches wide, 5 feet high, and 12 feet long. What is the capacity of the water tank in cubic feet? In gallons?

Example 2 image

Step 1. Use the equation for determining the volume of a rectangle. V = l × w × h

Step 2. Identify the length, width, and height. l = 12 ft, w = 34 in, h = 5 ft

Step 3. Convert all the measurements to the same units, feet.

Inches to Feet
Step 4. Set up the problem, and solve for volume. V = 2.83 ft × 5 ft × 12 ft = 170 ft3

Step 5. Set up the cancellation table so all units will cancel, except the desired unit, gallons.

Ft3 to Gallons

The volume of the tank is 170 cubic feet or 1272 gallons.

VOLUME OF A CYLINDER

The volume of a cylinder is found by multiplying the area of the base times the height, h. The base of a cylinder is a circle, A = π × r2, where π = 3.14. 

Volume Example

Example 3 - A cylindrical tank of foam concentrate is 5 feet tall. The tank diameter is 2.5 feet. What is the capacity, in gallons, of the tank?

Step 1. Use the equation for determining the volume of a cylinder.
V = π r2 × h

Step 2. Draw a sketch. Label the height and diameter.

Height and Diameter

π = 3.14, r = 1/2 d = 1/2 × 2.5 ft = 1.25 ft, h = 5 ft

Step 3. Set up the problem and solve. V = 3.14 × (1.25 ft)2 × 5 ft = 24.5 ft3

Step 4. Set up the cancellation table so all units will cancel, except the desired unit, gallons.

Ft3 to Gallons

The tank capacity is 183.3 gallons.

 

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