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Question

A manufacturing company wants to minimize the cost of materials for a pop can which needs to hold 592 mL. Find the radius and height (in centimeters) of the cylindrical can with minimum surface area that holds this volume.

 

Thankyou for the help

Answer 1

Volume is

 

πr²h = 592

 

 

Surface area is

 

SA = 2πr² + 2πrh

 

 

Substitute the volume equation into the surface area equation so that the surface area is in terms of only r. 

 

From the volume equation,

 

h = 592 / πr²

 

 

Perform the substitution.

 

Then once you've done that, set the derivative of SA equal to zero and solve for r.  The value of r is the radius that will minimize cost.  Then substitute that value of r into the volume equation to get your height.