Engineers are designing a box-shaped aquarium with a square bottom and an open top. The aquarium must hold 256 ft^3 of water. What dimensions should they use to create an acceptable aquarium with the least amount of glass?
Accepted Solution
A:
This is a calculus problem (in optimization). Let the aquarium dimensions be L, W and H. Then L*W*H = 256 ft^3. But W=L here, so W^2*H = 256 ft^3.
Write an expression for the area of the aquarium's glass sides and bottom.
So now we have A(W), the area as a function of W alone.
We want to minimize this area. To do this, differentiate A(W) with respect to W and set the result = to 0. We want to determine the "critical numbers."