SOLUTION: You have been asked to design a can shaped like a right circular cylinder with height h and radius r. Given that the can must hold exactly 410 cm3, what values of h and r will mini

Question 1033164: You have been asked to design a can shaped like a right circular cylinder with height h and radius r. Given that the can must hold exactly 410 cm3, what values of h and r will minimise the total surface area (including the top and bottom faces)? Give your answers correct to 2 decimal places as a list [in brackets] of the form: [ h, r ]
for constants h (height), r (radius), in that order.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
the volume of the cylinder with height and radius (both in cm) is

.
---> .
The total surface area (including the top and bottom faces)of a right circular cylinder with height and radius is
.
(We would measure and radius in cm, and would be in , of course).
Substituting the expression found for ,
<--> <--> .

We need to find the value of that yields the minimum for .
There may be another way to find that value.
Maybe you are expected to do it using a graphing calculator,
or maybe you are expected to use calculus,
and specifically derivatives.
The result should be the same.
Using calculus:
A local minimum of happens only for a value of that makes the derivative zero.
The derivative of is
.
<---><---> ---> (correct to 2 decimal places).
Then,
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