The image shows a rectangular box with dimensions:

• Height: 3 feet
• Length: 12 feet
• Width: 7 feet

The task is to find both the volume and the surface area of the box.

Volume of the box:

The volume $V$ of a rectangular box is given by: $V = \text{Length} \times \text{Width} \times \text{Height}$

Substituting the values: $V = 12 \, \text{ft} \times 7 \, \text{ft} \times 3 \, \text{ft} = 252 \, \text{cubic feet}$

Surface Area of the box:

The surface area $A$ of a rectangular box is calculated by summing the areas of all six faces. The formula is: $A = 2 \times (\text{Length} \times \text{Width} + \text{Width} \times \text{Height} + \text{Length} \times \text{Height})$

Substituting the values: $A = 2 \times (12 \, \text{ft} \times 7 \, \text{ft} + 7 \, \text{ft} \times 3 \, \text{ft} + 12 \, \text{ft} \times 3 \, \text{ft})$ $A = 2 \times (84 \, \text{sq ft} + 21 \, \text{sq ft} + 36 \, \text{sq ft}) = 2 \times 141 \, \text{sq ft} = 282 \, \text{square feet}$

Final Answer:

• Volume: 252 cubic feet
• Surface Area: 282 square feet

Do you have any further questions or need more details?

Here are 5 related questions:

1. How would the volume change if the height of the box were doubled?
2. What is the effect on the surface area if all dimensions are doubled?
3. How do you find the diagonal of the box?
4. How would you calculate the volume if the box had an open top?
5. What is the formula for surface area if the box is a cube?

Tip: Always double-check that the units of all measurements are consistent when calculating volume or surface area.