If you cut out a square of side $x$ from each corner along one edge, how much total length is removed from that edge?

After cutting and folding, what is the height of the box? What is the new length along the original 18-inch side? What is the new width along the original 12-inch side?

Once you have expressions for the new length, width, and height in terms of $x$, multiply them to get $V(x)$, then look for the matching answer choice.

In Desmos, create three expressions to represent the dimensions after cutting:

• L = 18 - 2x (length)
• W = 12 - 2x (width)
• H = x (height) You can add a slider for x (for example, from 0 to 6) to see how these change.

In a new line, type V = L * W * H. This defines the volume in terms of the three dimensions you just entered, directly reflecting the box’s geometry.

Now look back at the multiple-choice options and identify which one matches the way Desmos is computing V from L, W, and H (multiplying height by the two reduced side lengths). The choice with the same structure is the correct function.

An open-top box is still a rectangular prism. Its volume is

So your entire job is to figure out the new length, width, and height after the squares are cut out and the sides are folded up.

The squares cut from each corner have side length $x$. When you fold up the flaps along the cuts, that side length $x$ becomes the height of the box.

So the height of the finished box is $x$.

The original cardboard is $18$ inches by $12$ inches.

• Along the 18-inch side, you cut out a square of side $x$ from the left corner and another of side $x$ from the right corner. That removes a total of $2x$ from the length:
  • New length $= 18 - 2x$.
• Along the 12-inch side, you do the same, removing $x$ from each end:
  • New width $= 12 - 2x$.

Now plug these three dimensions into the volume formula:

• Length: $18 - 2x$
• Width: $12 - 2x$
• Height: $x$

So the volume is

This matches choice A.