Applications of Differentiation

Hey, I got stuck in one of my handbook question. I'm having exam in three days, so if any one know how to solve it (it should be quite simple But I'm just dumb) please help me.

Question: A travelling rock band is having a trailer made to carry their equipment. The roadies say the trailer must have a square base, an open top, and a volume of 32 m^{3} . Find the dimensions (length of base side and the height) for the trailer to be made with the least amount of sheet metal.

What I did so far....

V=Height x X^{2 }where x = length of the square base

Since the volume is 32, i change the equation to 32=h x X^{2}

this give me the height in term of X of (32/X^{2})

I also differentiate the equation so dv/dx = 2xh = 64/x

Now I'm stuck and don't know how to continue

Best Regards

Re: Applications of Differentiation

You don't differentiate the volume equation. You are not trying to minimise the volume. You are trying to minimise the amount of sheet metal needed to make the trailer, so you want to minimise the SURFACE AREA. Can you get an equation for the surface area in terms of x?

Re: Applications of Differentiation

remember to consider the surface area of the trailer with open top.

Volume = h*x^2 = 32

Surface area S = x^2 + 4xh

Then differentiate Surface area for minimising