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i think r would be 4.07 but im not sure about h=

 Dec 6, 2020
 #1
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Idk 😂 

 Dec 6, 2020
 #2
avatar+114592 
+2

I looked at this the other  day, jenny....unless I blew a fuse (always possible)....I didn't  find any  max

 

Here's what I  did

 

h =  300/ (pi r^2)    →  h^2  =  (90000/ pi^2)r-4

 

Subbing   x for  r   we have  that

 

S   =  (pi * x)  ( x^2  +  (90000/pi^2)x-4 )^((1/2)

 

The Calculus is messy  but this graph  shows  that  there is  no  positive  x = r   that will  produce a max.....only  a  min

 

https://www.desmos.com/calculator/zpyqlutuoq

 

A radius of  ≈  4.07 cm    will produce a minimum surface area  of  ≈ 90.229 cm^2

 

h =  300 / ( pi * 4.072)  ≈  5.76  cm

 

P.S.   - check my math....I could have missed something 

 

cool cool cool

 Dec 6, 2020

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