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How many gallons of fuel will be contained in a rectangular-shaped tank which measures 2 feet in width, 3 feet in length, and 1 foot 8 inches in depth? (Note: 7.5 gallons = 1 cubic foot)

Answer :

The rectangular-shaped tank can contain 75 gallons of fuel.

To determine how many gallons of fuel can be contained in a rectangular-shaped tank, we need to follow these steps:

  1. Convert all measurements to feet:

    • The dimensions of the tank are given as 2 feet (width), 3 feet (length), and 1 foot 8 inches (depth).
    • First, convert the depth from feet and inches to feet only.
    • Since 8 inches is equivalent to [tex]\frac{8}{12}[/tex] feet, we calculate:
      [tex]1 \text{ foot} + \frac{8}{12} \text{ feet} = 1 + \frac{2}{3} = \frac{5}{3} \text{ feet}[/tex]
    • Therefore, the depth is [tex]1.6667 \text{ feet}[/tex] (using decimal approximation).

  2. Calculate the volume of the tank in cubic feet:

    • The volume [tex]V[/tex] of a rectangular prism (the tank) can be found by using the formula:
      [tex]V = \text{length} \times \text{width} \times \text{depth}[/tex]
    • Applying the dimensions, we get:
      [tex]V = 3 \text{ ft} \times 2 \text{ ft} \times \frac{5}{3} \text{ ft}[/tex]
    • This simplifies to:
      [tex]V = 3 \times 2 \times 1.6667 = 10 \text{ cubic feet}[/tex]

  3. Convert cubic feet to gallons:

    • We know that 1 cubic foot is equivalent to 7.5 gallons.
    • Thus, to find the total volume in gallons, we multiply the volume in cubic feet by 7.5:
      [tex]\text{Gallons} = 10 \text{ cu ft} \times 7.5 \text{ gal/cu ft}[/tex]
    • Therefore:
      [tex]\text{Gallons} = 75 \text{ gallons}[/tex]

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Rewritten by : Barada