A lidless box with square ends

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Question from Chris:

A lidless box with square ends is to be made from a thin sheet of metal. Determine the least area of the metal for which the volume of the box is 3.5m^3.
I did this question and my answer is 11.08m^2 is this correct? If no can you show how you got the correct answer.

Hi Chris,

I got 11.41 m².

I let the dimensions of the box be x m by x m by y m so x² y = 3.5 m³ and thus y = 3.5/x² m. The surface area is then

A(x) = 2x² + 3xy = 2x² + 10.5/x

This gives

A'(x) = 4x - 10.5/x²

which I set equal to zero and found x to be the cube root of 10.5/4.

Is this what you did?

Harley

Chris,

Stephen wrote to me.

Harley, I got 10.98

Isn't A(x) = x² + 4xy = x² + 14/x ?

Do you see what he did?

It depends on the dimensions of the lid. Is the lid x by y? That's what I thought. Is it x by x? That's Stepnens solution.

Harley

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