The problem involves finding the total volume $V$ of a tower made by stacking 12 identical rectangular blocks. Each block has:

• Length: $2x$ inches
• Width: $x$ inches
• Height: $(x - 1)$ inches

The volume of one block is given by:
$\text{Volume of one block} = \text{Length} \times \text{Width} \times \text{Height} = (2x)(x)(x - 1) = 2x^2(x - 1)$

Since there are 12 blocks, the total volume $V$ of the tower is: $V = 12 \times \text{Volume of one block} = 12 \times 2x^2(x - 1)$

Simplify: $V = 24x^2(x - 1)$

Thus, the correct equation representing the volume of the tower is: $\boxed{V = 24x^2(x - 1)}$

Let me know if you'd like further explanation!

Relative Questions:

1. How is the volume of a rectangular prism calculated?
2. Why is the volume of the block multiplied by 12 to get the total volume?
3. How would the formula change if the number of blocks were different?
4. Can the height of the block, $x - 1$, affect the tipping point of the tower?
5. What would happen to the volume if $x$ were smaller than or equal to 1?

Tip:

Always double-check the dimensions (length, width, height) before calculating the volume of a prism to avoid mixing up the terms.