1. Cube:
Volume-to-surface-area ratio = V/S.A. = s/6
Sphere:
Volume-to-surface-area ratio = V/S.A. = (3/r)
Cylinder:
Volume-to-surface-area ratio = V/S.A. = (h/r + 2)/2
2. Based on the ratio, the best shape for an ice cube would be a sphere, as it has the lowest volume-to-surface-area ratio. The best size for this sphere-shaped ice cube would be small enough to fit in a glass of drink, but large enough to provide sufficient cooling.
3.
a. It is better for an ice cube to have a low volume, as it will melt faster and cool the drink more quickly.
b. It is better for an ice cube to have a small surface area, as it will take longer for the heat to melt the ice.
c. For an ice cube, the lowest possible volume-to-surface-area ratio would be better, as it would allow for faster cooling of the drink.
d. Increasing the size of an object increases its volume much more than its surface area, resulting in a higher volume-to-surface-area ratio.
4. Visual model: A small sphere-shaped ice cube with a diameter of 3 cm would have a volume of approximately 14 cubic centimeters and a surface area of approximately 28 square centimeters. This would make it an effective and efficient ice cube for cooling a drink.
[Insert image of sphere-shaped ice cube with dimensions and calculations]