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

#1**+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**+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

CPhill
May 17, 2017