A rectangular tank with a square base, an open top, and a volume of 10,976 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.

Now, the amount of material used is directly proportional to the surface area, hence we will minimize the amount of material by minimizing the surface area.

The formula for the surface area of the box described is given by;

A = x² + 4xh

However, we need A as a function of

only x, so we'll use the formula;

V = x²h

V = x²h = 10,976 ft³

So,

h = 10976/x²

So,

A = x² + 4x(10976/x²)

A = x² + 43904/x

So, to minimize the area, it will be at dA/dx = 0.

So,

dA/dx = 2x - 43904/x² = 0

Factorizing out, we have;

2x³ = 43904

x³ = 43904/2

x³ = 21952

x = ∛21952

x = 28 ft

since, h = 10976/x²

h = 10976/28² = 14 ft

Thus,dimension to minimize surface are is 28 ft x 28 ft x 14 ft

A rectangular tank with a square​ base, an open​ top, and a volume of 10,976 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.

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A rectangular tank with a square base, an open top, and a volume of 10,976 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.