Question

A company needs to create a concrete foundation 3 feet deep measuring 56‘ x 26‘, outside dimensions, with walls 5 inch thick how many cubic yards of concrete will they need?

Answer 1

We are asked to determine the volume of the concrete wall with the given dimensions. To do that we will determine the volume of the exterior prism with dimensions 56ft, 26ft, and 3ft. This volume is given by the product of its dimensions:

`V_e=(56ft)(26ft)(3ft)`

Solving the operations we get:

`V_e=4368ft^3`

Now, we need to determine the interior volume. That is the prism that is inside the foundation. To determine the dimensions we need to convert 5 inches to feet. To do that we will use the following conversion factor:

`1ft=12in`

Multiplying by the conversion factor we get:

`5in*(1ft)/(12in)=0.42ft`

Now we determine the length and width of the inside prism. To do that we use the following:

Therefore, we need to subtract 2 times 5 inches to each of the exterior dimensions to get the inner dimensions, therefore, the interior volume is:

`V_i=(56ft-2(5in))(26ft-2(5in))(3ft)`

Substituting the inches we get:

`V_i=(56ft-0.83ft)(26ft-0.83ft)(3ft)`

Solving the operations:

`V_i=4165.89ft^3`

Now, the volume of the wall is the difference between the exterior volume and the interior volume. Therefore:

`V=V_e-V_i`

Substituting the values we get:

`\begin{gathered} V=4368ft^3-4165.89ft^3 \\ V=202.11ft^3 \end{gathered}`

Since we need to express the solution in cubic yards we will use the following conversion factor:

`1yd^3=27ft^3`

Multiplying by the conversion factor we get:

`202.11ft^3*(1yd^3)/(27ft^3)=7.49yd^3`

Therefore, 7.5 cubic yards are needed.