SOLUTION: I was given a project to take a rectangular prism (like a cereal box)and get all the dimensions(length width height). we did that. now we have to make our own cereal box. they are

Algebra ->  Surface-area -> SOLUTION: I was given a project to take a rectangular prism (like a cereal box)and get all the dimensions(length width height). we did that. now we have to make our own cereal box. they are       Log On


   

Question 417454: I was given a project to take a rectangular prism (like a cereal box)and get all the dimensions(length width height). we did that. now we have to make our own cereal box. they are asking us to maximize the volume while minimizing the surface area. we can not figure out how to do this.
the original box- length 7.75 - width 5.5 - height 10.75
volume is 458.22 - surface area is 370.13 - surface area to volume ratio is 0.81
we have done all the work we just need to know how to increase the volume while decreasing the surface area.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I was given a project to take a rectangular prism (like a cereal box)and get all the dimensions(length width height).
we did that.
now we have to make our own cereal box.
they are asking us to maximize the volume while minimizing the surface area.
we can not figure out how to do this.
:
the original box- length 7.75 - width 5.5 - height 10.75 volume is 458.22 -
surface area is 370.13 - surface area to volume ratio is 0.81
;
You get max volume with min surface area if the box is a perfect cube
Find the cube root of 458.22, it's about 7.71 in on each side
:
A box 7.71 by 7.71 by 7.71 will have a surface area of:
6(7.71^2) = 356.66 sq/in
:
Surface/Vol: 356.66/458.22 ~.78