Question

How many gallons of the water are in the filled tank? You must show work with dimensional analysis using the above fact.

Answer 1

From the question, we can deduce the following:

Length = 5.6 meters

Width = 7.3 meters

Height = 4.5 meters

Where:

1 ft = 0.3048 m

1 cubic foot = 7.48 gallons

Let's find the amount of gallons of water in the tank if the tank is filled to 1 foot below the top of the tank.

Let's first sketch the tank.

We have:

Now, let's find the volume of the tank(total amount of water it can carry).

Apply the formula:

`V=l* w* h`

Thus, we have:

`\begin{gathered} V=5.6*7.3*4.5 \\ \\ V=183.96m^3 \end{gathered}`

Now, to find the amount of water presently in the tank since it is filled 1 ft below the top of the tank, we have:

`\begin{gathered} V=5.6*7.3*(4.5-0.3048) \\ \\ V=5.6*7.3*4.1952 \\ \\ V=171.5m^3 \end{gathered}`

Therefore, the volume of the water in the tank is 171.5 cubic meters.

Now, let'c convert from cubic meters to gallons.

Where:

1 foot = 0.3048 m

`1meter=(1)/(0.3048)=3.28\text{ feet}`

Thus, we have:

`\begin{gathered} 1\text{ cubic meter = 3.28}^3=35.29\text{ cubic f}eet \\ \\ 171.5\text{ cubic meters = 171.5 x 35.29 = }6052.235\text{ cubic fe}et \end{gathered}`

Now, to convert from cubic feet to gallons, where:

1 cubci foot = 7.48 gallon

We have:

`6052.235*7.48=45273.86\text{ gallons}`

Therefore, there are 45273.86 gallons of water filled in the tank.