A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 4.5 ft by 7 ft by 12 ft. The container is entirely full. If, on average, its contents weigh 0.7 pounds per cubic foot, and, on average, the contents are worth $2.00 per pound, find the value of the container’s contents. Round your answer to the nearest cent.

To solve this problem, we need to determine the value of the container's contents by calculating the following steps:

### Step 1: Find the volume of the container
The container is shaped like a right rectangular prism. The volume $ V $ of a right rectangular prism is given by the formula:

\[
V = \text{length} \times \text{width} \times \text{height}
\]

Using the dimensions provided:

\[
V = 4.5 \, \text{ft} \times 7 \, \text{ft} \times 12 \, \text{ft} = 378 \, \text{cubic feet}
\]

### Step 2: Calculate the total weight of the contents
The problem states that, on average, the contents weigh 0.7 pounds per cubic foot. To find the total weight, multiply the volume by the average weight per cubic foot:

\[
\text{Total weight} = 378 \, \text{cubic feet} \times 0.7 \, \frac{\text{pounds}}{\text{cubic foot}} = 264.6 \, \text{pounds}
\]

### Step 3: Calculate the total value of the contents
We are told that, on average, the contents are worth $2.00 per pound. Therefore, the total value is the total weight multiplied by the value per pound:

\[
\text{Total value} = 264.6 \, \text{pounds} \times 2.00 \, \frac{\text{dollars}}{\text{pound}} = 529.20 \, \text{dollars}
\]

Thus, the value of the container's contents is **$529.20**.

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the total value change if the contents weighed 0.8 pounds per cubic foot?
2. What is the total weight if the container dimensions were doubled?
3. How would the value change if the price per pound increased to $2.50?
4. What would happen to the volume if one dimension increased by 50%?
5. How would you calculate the surface area of the container?

**Tip:** Remember to keep track of your units, especially when dealing with volume, weight, and price per unit.

Learn how to calculate the value of contents in a transatlantic shipping container with dimensions 4.5 ft by 7 ft by 12 ft, using volume, weight per cubic foot, and price per pound. This problem covers key geometry concepts and is suitable for Grades 6-8.

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