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A rectangular prism is being designed to have a volume of 36 cubic units. Find the minimum surface area in square units for the prism if the edge lengths are positive integers.

 Feb 3, 2019
 #1
avatar+104836 
+2

I remember having such a problem in my Calculus class, but I've slept since then and I don't remember the procedure for solving it....however.....I believe the surface area is minimized when each dimension is = ∛36 units

 

So...the minimum surface area is

 

2  [  (∛36)^2 + (∛36)^2 + (∛36)^2 ]  ≈ 65.416 units^2

 

Maybe someone else on here knows the procedure

 

 

cool cool cool

 Feb 3, 2019
 #2
avatar+6045 
+2

The question specifies integer dimensions.

 

Basically you want as close to a cube as possible given integer dimensions that give a volume of 36.

 

4x3x3 is as close as you get.

Rom  Feb 3, 2019

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