First we calculate the volume of the foundation:
Volume (V) = 20 ft * 12 ft * 4 in (1 ft / 12 in)
V = 80 ft^3
Since the cost is in cubic yard (yard^3) so convert:
V = 80 ft^3 * (1 yard^3 / 27 ft^3) = 2.963 yard^3
So the total cost is:
cost = ($125 / yard^3) * 2.963 yard^3
cost = $370.37
Answer:
$370.37.
Step-by-step explanation:
We have been given that 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.
First of all, we will convert the given dimensions of foundation in yards.
[tex]\text{3 feet}=\text{1 yard}[/tex]
[tex]20\text{ feet}=\frac{20}{3}\text{ yards}[/tex]
[tex]12\text{ feet}=\frac{12}{3}\text{ yards}[/tex]
[tex]\text{36 inches}=\text{1 yard}[/tex]
[tex]\text{4 inches}=\frac{4}{36}\text{ yards}=\frac{1}{9}\text{ yards}[/tex]
Since the foundation of building is in form of cuboid, so volume of foundation will be the product of 3 sides.
[tex]\text{Volume of foundation}=\frac{20}{3}\text{ yards}\times \frac{12}{3}\text{ yards}\times \frac{1}{9}\text{ yards}[/tex]
[tex]\text{Volume of foundation}=\frac{20\times 12\times 1}{3\times 3 \times 9}\text{ yards}^3[/tex]
[tex]\text{Volume of foundation}=\frac{240}{81}\text{ yards}^3[/tex]
[tex]\text{Volume of foundation}=2.962962962962963\text{ yards}^3[/tex]
Since the local home supply store sells concrete for $125 per cubic yard, so the cost of the concrete for the foundation will be the volume of foundation times $125.
[tex]\text{The cost of the concrete for the foundation}=2.962962962962963\text{ yards}^3\times \frac{\$125}{\text{ yards}^3}[/tex]
[tex]\text{The cost of the concrete for the foundation}=\$370.37037\approx \$370.37[/tex]
Therefore, the cost of the concrete for the foundation is $370.37.
