1. Find and simplify the volume-to-surface-area ratio for each of the three
possible ice cube shapes. You can use this chart.
Shape Surface Area Formula Volume Formula
cube
2
S.A. 6 s^2
3 V s
sphere
2
S.A. 4 r
4 3
3
V r
cylinder
2
S.A. 2 2 r rh 2 V r h
2. Use the ratios to choose the best shape for an ice cube—a cube, sphere, or
cylinder. Also, choose what you think is the best size for that shaped ice
cube.
3. Consider these questions as you make your decision:
a. Since the purpose of an ice cube is to keep a drink cold, is it better for
an ice cube to have a high volume or a low volume?
b. Since heat touching the surface of an ice cube causes it to melt, is it
better for an ice cube to have a large surface area or a small surface
area?
c. Which volume-to-surface-area ratio would be better for an ice cube—
the lowest possible or the highest possible?
d. How does increasing the size of an object affect its volume-to-surface-area ratio?
4. Create a visual model to show your ice cube design, including the dimensions
you would choose and the volume and surface area of that cube.
Your visual model and the explanation of your choice of ice cube shape and size will
be submitted as your portfolio assessment.
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]