Acompany is constructing an open-top, square-based, rectangular metal tank that will have a volume of 64 ft3. what dimensions yield the minimum surface area? round to the nearest tenth, if necessary.

The sides of the base of the tank: 5.03 feet

The height of the tank: 2.52 feet

Step-by-step explanation:

Given:

Volume of an open-top, square-based, rectangular metal tank = 64

Let:

The side of the square base  = x ft

Height of the tank = y

So, The volume of the tank =

                                              ........(i)

And surface area =

From (i)

                  Surface area (SA)=

Now, Differentiate

                  (SA)' =

solve for , you obtain:

Now, you must calculate

Therefore, the dimensions are:

The sides of the base of the tank: 5.03 feet

The height of the tank: 2.52 feet

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To solve this problem you must apply the proccedure shown below:

1. You must use the formula for calculate the surface area and the volume of the tank:

2. Solve for in the second equation and substitute it into the first one.Then, you have:

3. Now, derivate:

4. When you solve for , you obtain:

5. Now, you must calculate :

Therefore, the dimensions are:

The sides of the base of the tank:

The height of the tank:

3/6   and 9/18

step-by-step explanation: