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. if the local home supply store sells concrete for $125 per cubic yard, what will be the cost of the concrete for the foundation?

Answer 1

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 2

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.

$\text{3 feet}=\text{1 yard}$

$20\text{ feet}=\frac{20}{3}\text{ yards}$

$12\text{ feet}=\frac{12}{3}\text{ yards}$

$\text{36 inches}=\text{1 yard}$

$\text{4 inches}=\frac{4}{36}\text{ yards}=\frac{1}{9}\text{ yards}$

Since the foundation of building is in form of cuboid, so volume of foundation will be the product of 3 sides.

$\text{Volume of foundation}=\frac{20}{3}\text{ yards}\times \frac{12}{3}\text{ yards}\times \frac{1}{9}\text{ yards}$

$\text{Volume of foundation}=\frac{20\times 12\times 1}{3\times 3 \times 9}\text{ yards}^3$

$\text{Volume of foundation}=\frac{240}{81}\text{ yards}^3$

$\text{Volume of foundation}=2.962962962962963\text{ yards}^3$

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.

$\text{The cost of the concrete for the foundation}=2.962962962962963\text{ yards}^3\times \frac{\ 125}{\text{ yards}^3}$

$\text{The cost of the concrete for the foundation}=\ 370.37037\approx \ 370.37$

Therefore, the cost of the concrete for the foundation is $370.37.