To make a square bottomless water tank with a volume of 256l, what's its height and material saving?

To make a square bottomless water tank with a volume of 256l, what's its height and material saving?

Let the height of the tank be x and the length of the bottom edge be a, then a 2x = 256 and its surface area s = 4ax + a 2 = 1024a + a 2 = 512a + 512a + a 2 ≥ 33512a × 512a × a 2 = 3 × 26 = 192. If and only if a = 8, that is, H ﹥ 4, s gets the minimum

To make a 256 liter square bottomless water tank, how high is the material most economical?
To the third power is sixteen? How to drive? Are you driving sixteen?

Set the height as X, the side length of the bottom √ (256 / x)
Surface area f (x) = 4x √ (256 / x) + 256 / x = 64 √ x + 256 / X
f'(x)=32/√x-256/x^2
Let f '(x) = 0, that is, 32 / √ x = 256 / x ^ 2, then x = 4
00, increasing gradually;
So f (x) has a minimum at x = 4

A cuboid water tank, low is a square, the height of the water tank is 4 decimeters, its side area is 40 square decimeters, how many square decimeters is the surface area of the water tank

As the height of the water tank is 4 decimeters, its side area is 40 square decimeters
So the length of the bottom edge is: 40 / 4 = 10 (decimeter)
So the surface area is: 2 * 10 * 10 + 40 * 4 = 360 cubic decimeter