I have a hollow metal cube that has an edge length of 10 cm. The walls of the cu

Question

I have a hollow metal cube that has an edge length of 10 cm.
The walls of the cube are 2 mm (or .2 cm) thick.
What is the volume of the metal required to make this cube?
You MUST use differentiation to find this volume.

I know that the top and bottom faces of the cube are 10 cm x 10 cm x .2 cm.
I know that the 4 other faces must be (10 cm - (2 * .2 cm)) x (10 cm - (2 * .2 cm)) x .2 cm, or 9.6 cm x 9.6 cm x .2 cm to account for thickness.

So, 10 x 10 x .2 = 20 cm3. (2 faces gives me 40 cm3)

And 9.6 x 9.6 x .2 = 18.432 cm3. (4 faces gives me 73.728 cm3)

The total should be 113.728 cm3. But how do I use calculus and differentiation to do this problem? I don't see any variables so I can't even write a function for volume!

Explanation / Answer

would have been easier for calculating volume directly is 10^3 - 9.6^3 = 115.26 You want to integrate surface area to give you volume. What is surface area here? The formula is 6x^2, you really only want x to increase in one direction though so consider this, you have a block with 24 squares on i.... https://s3.amazonaws.com/answer-board-image/363d3790-1564-4516-9675-e27cd77cf985.jpeg

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