# Math Help - [SOLVED] Help designing tank

1. ## [SOLVED] Help designing tank

The problem is: You have to design a 500ft^3 square-based, open-top, rectangular holding tank. It is to be made from stainless steel plates. Find the dimensions for the base and height that will make the tank weigh as little as possible.

I know that you take 500=h*x^2 and find that h=500/(x^2). Then I think you're supposed to plug it into the SA equation and get SA=(x^2)+4x[500/(x^2)], but I'm not sure and I keep on getting impossible answers after that.

2. Hi there smartartbug, happy new year!

I agree that $SA = x^2+4xh = x^2+2000x^{-1}$ after substitution

now $\frac{dSA}{dx}= 2x-\frac{2000}{x^2}$

Now set $\frac{dSA}{dx}=0$ and solve

Spoiler:

$0=2x-\frac{2000}{x^2}$

$\frac{2000}{x^2}=2x$

$1000=x^3$

$x=10$

3. Thank you so much! I totally missed that subtract 1 on the -1. So now I'm getting x=10 and h=5. I hope I did that last part right. Thanks again!

4. Originally Posted by smartartbug
So now I'm getting x=10 and h=5. I hope I did that last part right.