Question

I have to do this project which is worth 50% of my grade and part of the project is a question asking, "Which would be the best design for an ice cube?" The choices are a cube, a sphere, or a cylinder. I need to explain why I think which of them are best. Can somebody help me out with an example ?

Answer 1

The question is poorly worded.

"Which would be the best design for an ice cube?"
based on what?
Given some fixed surface area ?
- which is rather meaningless for an ice "cube"
Stability of storing?
- trays to freeze spherical ice "cubes" don't seem very efficient.
... etc

let's suppose our ice "cube" is to contain 100 cm^3

as a cube:
let each side be x
so x^3 = 100
x = appr 4.64 cm
surface area = 6(4.64)^2 = appr 129.3 cm^2

as a sphere:
(4/3)π r^3 = 100
r^3 = 300/(4π)
r = appr 2.88 cm
surface area = 4π(2.88)^2 = appr 104.2 cm^2

as a cylinder, with height = diameter
π r^2 r = 100
r^3 = 100/π
r = 3.169
Surface area = 2πr^2 + 2πr^2
= 4πr^2 = appr 126.2 cm^2

looks like for this criteria, the sphere would be "best"