Solution
- The concrete foundation is in the shape of a rectangular prism. The volume of a rectangular prism is:

- With the above formula, we can proceed to find the volume that the concrete foundation will occupy.
- Let us find this volume but we should convert all our units to yards because that is the unit the question is asking us to work in.
- The conversion of the dimensions is done below:
![\begin{gathered} 1\text{ yard}\to3\text{ feet} \\ 1\text{ yard}\to36\text{ inches} \\ \\ \text{ Converting feet to yard:} \\ 20\text{ feet to yards:} \\ \frac{1\text{ yard}}{3\text{ feet}}=\frac{x\text{ yards}}{20\text{ feet}} \\ \\ \text{ Cross Multiply,} \\ x=\frac{20\text{ feet}*1yard}{3\text{ feet}} \\ \\ x=(20)/(3)yards \\ \\ \text{ Thus, 20 feet corresponds to }(20)/(3)\text{ yards} \\ \\ 12\text{ feet to yards:} \\ \frac{1\text{ yard}}{3\text{ feet}}=\frac{x\text{ yards}}{12\text{ feet}} \\ \\ \text{ Cross Multiply,} \\ x=(12*1)/(3) \\ \\ x=4yards \\ \text{ Thus, 12 feet corresponds to 4 yards} \\ \\ \\ \text{ Converting inches to yards:} \\ \frac{1yard}{36\text{ inches}}=\frac{x}{4\text{ inches}} \\ \\ \text{ Cross Multiply,} \\ x=(4*1)/(36) \\ \\ x=(1)/(9)\text{ yards} \\ \\ \text{ Thus, 4 inches corresponds to }(1)/(9)\text{ yards} \end{gathered}]()
Question 11:
- Thus, let us now calculate volume of the concrete foundation. This is done below:

- The volume of concrete needed is 2.96 cubic yards
Question 12:
- We are told that 1 cubic yard of concrete sells for $125. This means that the cost of concrete required for the foundation can be gotten by simply multiplying the cost per cubic yard of concrete, by the amount of concrete needed.
- This is done below

- The cost of the concrete will be approximately $370
Final Answer
The volume of concrete needed is 2.96 cubic yards
The cost of the concrete will be approximately $370