Engineers are designing a box-shaped aquarium with a square bottom and an open top. The aquarium must hold 864 ft^3 of water. What dimensions should they use to create an acceptable aquarium with the least amount of glass?

Question

melich · Answer

The answer is 12 in by 12 in by 6 in but I don't know how to solve it.

legomyego180 · Answer

Do you know how to solve optimization problems?

melich · Answer

some

legomyego180 · Answer

First Step is to draw a picture|dw:1463441543100:dw|

legomyego180 · Answer

Next figure out a formula for volume

in this case because we have a square base we can use the formula x^2*h

melich · Answer

I got it thanks

legomyego180 · Answer

Cool, we've got our formula, but we arent quite ready to start doing calculus yet. We need to set our constraint. Lets find out what h is in terms of x for this problem

$$864=x^2*h$$
$$h=\frac{ 864 }{ x^2 }$$

legomyego180 · Answer

sweet np