Arectangular tank that is 4000 ft cubed with a square base and open top is to be constructed of sheet steel of a given thickness. find the dimensions of the tank with minimum weight.

dimension is 20ft*20ft*10ft

Explanation:

let a,a and h are length, width and height of given tank with square base.

volume = a*a*h

surface area =aa +2(ah+ah)

for weight to minimize, surface area is to be minimum i.e.

a = 20ft

now

at a = 20 ft

h = 10ft

hence dimension is 20ft*20ft*10ft

dimension of the rectangular tank = (20 ft × 20 ft × 10 ft)

Explanation:

volume of rectangle = 4000 ft³

volume of the tank = a² × h

surface area of the tank = 4 × a × h + a²

from the volume of the tank h = 4000/a²

now surface area becomes

now ,

h = 10 ft.

hence, the dimension of the rectangular tank comes out to be

(20 ft × 20 ft × 10 ft)

a

explanation:

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