Arectangular tank with a square base, an open top, and a volume of 864 ft cubed is to be constructed of sheet steel. find the dimensions of the tank that has the minimum surface area. let s be the length of one of the sides of the square base and let a be the surface area of the tank. write the objective function.

Tank dimensions:

s = 12 ft

h = 6 ft

Step-by-step explanation:

s = lenght side of the square base

A the total area of of the tank  ( this area is the area of the base plus  the lateral area (4) times

h  = the height of the tank

V  = 864 ft³             V  =  s² * h    ⇒   h = V/s²  ⇒ h = 864/ s²

Then we have :

A (total) =  Base area + 4 * lateral area

Area of the base is  s²

Lateral area is  s * h  but we have 4 wall  so lateral area = 4*s*h

Then Objective function is :

A(s) = s² + 4*s * V/s²           ⇒    A(s) = s²  + 4*864/s     ⇒   A(s) = s²  + 3456/s

Taken derivative of the objective function:

A´(s) = 2s - 3456/ s²

Solving for s

2s - 3456/s²  = 0     ⇒  2*s³  - 3456 = 0   ⇒  s³  = 3456/2  ⇒ s³ =  1728

s = ∛1728      ⇒   s =  12 ft

So h = V/s²       ⇒  h = 864 / 144       ⇒  h = 6 ft

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.

answer: 414,377,008

step-by-step explanation:

just multiply it