Question

The typical soft drink can in the U.S. has a volume of 355 cm³. The two circular ends cost $0.0006 per cm² each (because they are thicker), and the cost of the aluminum for the side of the can is $0 00028 per cm2. What dimensions will minimize the cost of a can? (Round your answers to two decimal places.)

Answer 1

Step-by-step explanation:

To minimize cost, is to reduce cost to the barest minimum.

The dimensions that minimize the cost of a can are: radius of 2.90 cm and a height of 39.02 cm

Given

--- volume of the can

--- the cost of the circular ends

--- the cost of the side

The soft drink can, has the shape of a cylinder.

The volume of the can is:

So, we have:

Make h the subject

The surface area of the can is:

The cost of the can is then calculated as:

Substitute

Substitute and

Rewrite as:

Differentiate

Set to 0

Rewrite as:

Multiply through by

Solve for

Take cube roots of both sides

Recall that:

Hence, the dimensions that minimize the cost of a can are:

and

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