Question

I arrive home to find that my 50 foot by 40 foot basement has 18 inches of water in it. What is the volume of water in my basement in cubic feet?What is the volume in cubic inches?

Answer 1

- To better visualize the problem, let us draw a sketch of the scenario. This is shown below:

- From the above, we can see that the water column occupies the whole width and length of the basement and rises to a height of 18 inches.

- Thus, to find the volume of water in the basement, we simply use the formula for the volume of a rectangular prism.

- The volume of a rectangular prism is

`\begin{gathered} V=l* w* h \\ where, \\ l=\text{ Length of the basement} \\ w=\text{ Width of the basement} \\ h=\text{ Height of the water column} \end{gathered}`

- But before we proceed to apply the formula, we need to make sure that all our dimensions are in the same unit.

- We have 40 feet by 50 feet floor in the basement but the water column is at a height of 18 inches.

- Since we are asked to find the volume of water in both cubic feet and cubic inches, we should convert our dimensions to purely feet and purely inches and make our calculations.

- The conversion is done below:

`\begin{gathered} 1\text{ foot}\to12\text{ inches} \\ \\ \text{ Thus, we can say:} \\ \frac{1\text{ foot}}{12\text{ inches}}=\frac{x\text{ feet}}{18\text{ inches}} \\ \\ \text{ Cross Multiply,} \\ x\text{ feet}=\frac{18inches*1foot}{12\text{ inches}} \\ \\ x=1.5feet \\ \text{ This means the height of the water column was 1.5feet} \\ \\ \\ \text{ Also,} \\ \frac{1\text{ foot}}{12\text{ inches}}=\frac{50\text{ feet}}{x\text{ inches}} \\ \\ Cross\text{ Multiply,} \\ x\text{ inches}=(50*12)/(1)=600\text{ inches} \\ (This\text{ means 50 feet corresponds to 600 inches\rparen} \\ \\ And, \\ \frac{1\text{ foot}}{12\text{ inches}}=\frac{40\text{ feet}}{x\text{ inches}} \\ \\ \text{ Cross Multiply,} \\ x\text{ inches}=(12*40)/(1)=480\text{ inches} \\ (\text{ This means that 40 feet corresponds to 480 inches\rparen} \end{gathered}`

- Now that we are done with the conversions, we can proceed to find the volume of water in the basement in both units.

- This is done below:

`\begin{gathered} \text{ In feet:} \\ l=50ft \\ w=40ft \\ h=1.5ft \\ \\ \therefore V=(50*40*1.5)ft^3 \\ V=3000ft^2 \\ \\ \\ \\ \text{ In inches:} \\ l=600inches \\ w=480inches \\ h=18inches \\ \\ \therefore V=(600*480*18)inches^3 \\ V=5,184,000inches^3 \end{gathered}`

Final Answer

The volume of the water in the basement in cubic feet and cubic inches is:

`\begin{gathered} V=3000ft^3 \\ \\ V=5,184,000inches^3 \end{gathered}`