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what would the lowest surface area for a prism with a volume of 100 meters cubed??? 

(using only whole numbers for dementions)

football.girl.40  May 17, 2017
edited by football.girl.40  May 17, 2017
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3+0 Answers

 #1
avatar+90641 
+2

what would the lowest surface area for a prism with a volume of 100 meters cubed??? 

(using only whole numbers for dementions)

 

The lowest surface area would be if the sides were all the same.

 

side length = 100^(1/3) = 4.641588833612778m        

 

So the surface area would be   6*(100^(1/3))^2 = 129.2660814019129736   cm^2

 

this is the same as 6*4.641588833612778^2

or

the same as      6*(100^(2/3))

Melody  May 17, 2017
 #2
avatar+77243 
+2

 

I'm just  playing around with this......I don't know if it's correct....

 

L * W * H

Volume

Surface Area

 

1 * 1 * 100  m^3

2 ( 1  + 100 + 100) =  400  m^2

 

2 * 2 * 25 =  100m^3

2 ( 4 + 50 + 50)  = 208  m^2

 

2 * 5 * 10   = 100 m^3

2( 20 + 10 + 50)  =  160 m^2

 

5 * 5 * 4 =  100 m^3

2(25 + 20 + 20)  =  130 m^2

 

WolframAlpha  shows that the surface area is minimized when each dimension ≈ 4.64159 m

And the surface area ≈ 129.266 m^2 

 

Which is exactly what Melody got........

 

But.....since each dimension must be an integer.........

 

I'm assuming that my last answer must be pretty close, since the surface area  = 130 m^2

 

That is.....we have  a square base of 5m on each side  and a height of 4 m

 

 

 

cool cool cool

CPhill  May 17, 2017
edited by CPhill  May 17, 2017
edited by CPhill  May 17, 2017
 #3
avatar+90641 
+1

Thanks Chris, I didn't see the interger bit.  :/

 

So yes you need three integers that are as close as posible to the same value, that multiply to give 100.

Melody  May 17, 2017

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