Short Answer 
The volume of a prism is calculated using the formula V = lw h, where l, w, and h are expressions based on the variable d. After substituting and simplifying these expressions, the final volume formula is V = 3(d Р4)², allowing for easy calculation when d is known.
Step 1: Understanding the Volume Formula
The volume of a prism is calculated using the formula V = lw h, where:
- l represents the length
- w represents the width
- h represents the height
In this case, we have specific expressions for length, width, and height based on the variable d:
- l = 3d – 9d – 2
- w = d – 4
- h = 2d – 4
Step 2: Substituting Variables
Now, we substitute the expressions for length, width, and height into the volume formula:
V = (3d – 9d – 2)(d – 4)(2d – 4). By simplifying this through replacements:
- Combine terms: V = (3d – 9)(d – 4)(d – 2)(4(d – 3))
We will further condense the expression to prepare for final calculations.
Step 3: Final Simplification
After performing the simplifications, we arrive at the final expression for volume:
- V = 3(d Р4)²
This final expression represents the volume of the prism in terms of the variable d, making it easier to compute when the value of d is known.