Question

. A general contractor is constructing a building that requires a concrete foundation that is to be 20 feet by 12 feet and 4 inches thick.11. How many cubic yards of concrete do you need? (round to the hundredths place)12. If the local home supply store sells concrete for $125 per cubic yard, what will be the cost of the concrete for thefoundation? (round to the nearest whole number)

Answer 1

Solution

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

$\begin{gathered} V=l\times w\times h \\ where, \\ l=length\text{ of the prism} \\ w=width \\ h=\text{ This is the height or thickness of the prism} \end{gathered}$

- 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:

$\begin{gathered} 1\text{ yard}\to3\text{ feet} \\ 1\text{ yard}\to36\text{ inches} \\ \\ \text{ Converting feet to yard:} \\ 20\text{ feet to yards:} \\ \frac{1\text{ yard}}{3\text{ feet}}=\frac{x\text{ yards}}{20\text{ feet}} \\ \\ \text{ Cross Multiply,} \\ x=\frac{20\text{ feet}\times1yard}{3\text{ feet}} \\ \\ x=\frac{20}{3}yards \\ \\ \text{ Thus, 20 feet corresponds to }\frac{20}{3}\text{ yards} \\ \\ 12\text{ feet to yards:} \\ \frac{1\text{ yard}}{3\text{ feet}}=\frac{x\text{ yards}}{12\text{ feet}} \\ \\ \text{ Cross Multiply,} \\ x=\frac{12\times1}{3} \\ \\ x=4yards \\ \text{ Thus, 12 feet corresponds to 4 yards} \\ \\ \\ \text{ Converting inches to yards:} \\ \frac{1yard}{36\text{ inches}}=\frac{x}{4\text{ inches}} \\ \\ \text{ Cross Multiply,} \\ x=\frac{4\times1}{36} \\ \\ x=\frac{1}{9}\text{ yards} \\ \\ \text{ Thus, 4 inches corresponds to }\frac{1}{9}\text{ yards} \end{gathered}$

Question 11:

- Thus, let us now calculate volume of the concrete foundation. This is done below:

$\begin{gathered} l=\frac{20}{3}yards \\ w=4yards \\ h=\frac{1}{9}yards \\ \\ \therefore V=l\times w\times h=\frac{20}{3}\times4\times\frac{1}{9} \\ \\ V=\frac{80}{27}yards=2.96296296...\approx2.96\text{ \lparen To the nearest hundredths\rparen} \end{gathered}$

- 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

$\begin{gathered} \ 125per\text{ yard}\times\frac{80}{27}yards \\ \\ =\ \frac{10,000}{27}=370.370370370...\approx370\text{ }(To\text{ the nearest whole number\rparen} \end{gathered}$

- 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