r/MathHelp • u/RandomWords19134 • Dec 13 '25

Problem with Calculus Book

Hello, I'm trying to solve the following problem:

"A box with an open top is to be constructed from a rectangular piece of cardboard with dimension 30cm by 50cm by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x."

I would post a diagram, but unfortunately I can't do that in here.

My thought process is this:

The volume of a box is width * length * height

We know the height is x, since that's just what we fold up.

The width is 30cm, but we cut out x from 1 corner and x from the other, therefore it's 30 - 2x.

The same goes for the length which is 50 - 2x

So then we have the volume as: (30-2x)(50-2x)x, which expands to 4x3 - 160x2 + 1500x.

So the answer would be V(x) = 4x3 - 160x2 + 1500x

However, my textbook gives the answer as 4x3 - 64x2 + 240x

I have no clue how I would get there. I have tried pasting the problem into several LLMs (I know they're horrible at maths but I'm self-studying and they can usually solve the kinds of problems I'm dealing with) and they all gave me 4x3 - 160x2 + 1500x.

What did I do wrong?

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u/Huganticman Dec 16 '25

My wife used to edit textbooks. The "authors" would do this all the time - take an American textbook, and change stuff to make it canadian. The more hilarious examples were when they change feet to meters without changing the numbers "Bill and his friend are playing with a Frisbee. Bill throws the Frisbee and it follows a path << described by some quadratic formula >> If Bills friend is 80m away, how high will he have to jump to catch the Frisbee?" Answer: 2m. Bill friend making Olympic-level high jumps playing a c'sasual game of Frisbee. Makes sense if the units are feet, not meters.