Question

A rectangular prism with a length of 40 feet, width of 8 feet, and height of 9 feet.
Mr. Newman hired painters to paint two storage containers similar to the one shown. If each can of paint costs $15 and will cover 188 square feet, how much will it cost to paint both containers?
$108
$120
$230
$240

Answer 1

To find the cost to paint both storage containers, we first need to calculate the surface area of one rectangular prism and then determine the total area to be painted for two containers. After that, we can calculate the number of paint cans needed and the total cost.

1. **Calculate the surface area of one rectangular prism**:

The formula for the surface area \( A \) of a rectangular prism is:

\[
A = 2(lw + lh + wh)
\]

where:
- \( l \) = length
- \( w \) = width
- \( h \) = height

Substituting the given dimensions (length = 40 feet, width = 8 feet, height = 9 feet):

\[
A = 2(40 \cdot 8 + 40 \cdot 9 + 8 \cdot 9)
\]

Calculating each term:

- \( lw = 40 \cdot 8 = 320 \)
- \( lh = 40 \cdot 9 = 360 \)
- \( wh = 8 \cdot 9 = 72 \)

Now sum these values:

\[
320 + 360 + 72 = 752
\]

Now, multiply by 2 for the total surface area:

\[
A = 2 \cdot 752 = 1504 \text{ square feet}
\]

2. **Calculate the surface area for two containers**:

\[
\text{Total surface area for two containers} = 2 \cdot 1504 = 3008 \text{ square feet}
\]

3. **Determine the number of cans of paint needed**:

Each can covers 188 square feet. To find the total number of cans needed:

\[
\text{Number of cans} = \frac{3008}{188}
\]

Calculating this:

\[
\frac{3008}{188} \approx 16
\]

Since you can't buy a fraction of a can, you will need to round up to the nearest whole number. Thus, you will need 16 cans.

4. **Calculate the total cost**:

Each can costs $15, so the total cost will be:

\[
\text{Total cost} = 16 \cdot 15 = 240
\]

Thus, the cost to paint both containers is:

\[
\boxed{240}
\]