Design a new cereal box that will hold the same amount of cereal but reduce manufacturing costs. Prove that your new design holds the same amount but can be manufactured more cheaply.
The original ceral box has a surface area of 312 sq. in and a volume of 288 in^3.
Any help would be much appreciated
+128408 Let the box be designed as a cube.....
Then....every dimension wlll = the cuberoot of the volume = cuberoot [ 288] ≈ 6.60 in
And the surface area will = 6 * side^2 = 6 * [cuberoot [288]]^2 ≈ 266.665 in^2
Thus, the volume is the same but the surface area [ and, hence, production cost] per box is reduced from 312 in^2 to 266.665 in^2
+36916 ANOTHER option: Make the package a CYLINDER (Like Quaker Oats)
Volume = pi r^2 h = 288 Let's make h = 10 then r = 3.0277
Area of the 'package' = pi d h = pi (6.0555) 10 = 190.233 sq in (but we must still add the two ends)
Area of Ends = 2 x pi r^2 = 2 x pi = 57.59
Total area of packaging = 57.59 + 190.233 = 247.823 sq in even LESS than a cube
Make the cylinder bigger (diameter) and shorter and save even MORE in packaging materials.
Cylinders will not be as efficient as a shipping option as a cube....though not far off!
