This is a rectangular prism with the given dimensions:

• Length: 12 inches
• Width: 8 inches
• Height: 6 inches

Let's calculate the surface area and volume of this solid.

1. Surface Area (SA) of a Rectangular Prism:

The formula for the surface area of a rectangular prism is:

$\text{SA} = 2lw + 2lh + 2wh$

Where:

• $l = 12$ inches (length)
• $w = 8$ inches (width)
• $h = 6$ inches (height)

Now plug in the values:

$\text{SA} = 2(12 \times 8) + 2(12 \times 6) + 2(8 \times 6)$ $\text{SA} = 2(96) + 2(72) + 2(48)$ $\text{SA} = 192 + 144 + 96 = 432 \, \text{square inches}$

2. Volume (V) of a Rectangular Prism:

The formula for the volume is:

$V = l \times w \times h$

Substitute the values:

$V = 12 \times 8 \times 6 = 576 \, \text{cubic inches}$

Final Answers:

• Surface area = 432 square inches
• Volume = 576 cubic inches

Would you like any further explanation or details on these calculations?

Related Questions:

1. How does the surface area change if the dimensions are doubled?
2. What is the ratio of surface area to volume in this prism?
3. Can you find the diagonal length of this rectangular prism?
4. How would the surface area change if the length, width, and height were all increased by 50%?
5. What would happen to the volume if the height were halved while the other dimensions stayed the same?

Tip:

When solving for surface area or volume of any prism, always check that the units are consistent before calculating.