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

b and c

step-by-step explanation: