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# Geometry~ im lost

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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
#1
+93654
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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)

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
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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

CPhill  May 17, 2017
edited by CPhill  May 17, 2017
edited by CPhill  May 17, 2017
#3
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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