# Thread: Functions of several variables

1. ## Functions of several variables

How do you go about solving this?

Find the dimension of the rectangular box of least surface area that has a volume of 1000 cubic inches.

2. Well i'm not sure if we have enough information to completely solve this.

But here's a start. Let's call the length, width and height of the box $l,w,h$ respectively.

This means we can obtain from the formula fr volume $V = l\times w \times h \implies 1000 = l\times w \times h$

Now from the rule for surface area we can say $SA = 2(lw+lh+hw)$

From here we get stuck. Is there any other information? I.e. like the length is equal to the width or something similar?

The idea here is to use one equation to help reduce the numer of variables in the other. The problem here is we have 3 variables and only 2 equations.