A rectangular tank with a square​ base, an open​ top, and a volume of 37044 ft^3 is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.

The dimensions of this rectangular tank that has the minimum surface area are 42 feet and 21 feet.How to calculate the dimensions of the tank that has the minimum surface area?First of all, we would determine the surface area of this rectangular tank with a square​ base by using this formula:h = V/s²Where:h represents the height of a rectangular tank.s represents the side of the square base.V represents the volume of a rectangular tank.For the surface area of this rectangular tank with a square​ base, we have:Surface area, A = base area + 4(lateral area)Surface area, A = s² + 4(s × h)Surface area, A = s² + 4(s × V/s²)Surface area, A = s² + 4V/sNext, we would take the first derivative of the surface area as follows:A' = 2s - 4V/s²Substituting the given parameters into the formula, we have;A' = 2s - 4(37044)/s²For the minimum surface area dimension, the first derivative of the surface area would be equated to zero:2s - 148,176/s² = 0148,176/s² = 2s148,176 = 2s³s³ = 74,088s = ∛74,088s = 42 feet.For the height, we have:Height, h = V/s²Height, h = 37044/42²Height, h = 37044/1764Height, h = 21 feet.Read more on minimum surface area here: https://brainly.com/question/13789217#SPJ1