A rectangular metal tank with an open top is to hold cubic feet of liquid. What are the dimensions of the tank that require the least material to%E2%80%8B build?

Step-by-step explanation:

Given

Required

The dimension that requires least material

The volume is:

Where:

So, we have:

Make l the subject

The surface area (A) of an open-top rectangular tank is:

Substitute:

Rewrite as:

Differentiate with respect to h and w

Equate both to 0

Make w the subject

Divide by 2

Make h the subject

Divide by 2

Substitute in

Multiply both sides by

Rewrite as:

Inverse both sides

Take cube roots

---- height

Recall that:

--- width

Recall that:

--- length

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you

.there can be infinite values of m and n that can satisfy the above equation. for each value of m of m or n. there maybe infinite sets of solution for the above

step-by-step explanation: