Math CentralQuandaries & Queries


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?



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.


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