Re: How does the shape of an ice cube affect how fast it melts?

Hello Jennifer,

The rate at which your ice melts does depend upon it's shape.  To be 
specific, different shapes have different amounts of surface area.  For 
example, your cube shaped ice has six squares on it's surface, where as 
the half-moon or half-cylinder shaped ice has two semicircles and two 
rectangles (one is straight and the other curved).  So even though both 
ice shapes have the same mass, density and volume, they have different 
amounts of surface area, depending upon the dimensions (length, height, 
radius) of the shapes.  By increasing the surface area, the rate of a 
process (such as ice melting) increases as more of the ice is exposed to 
the warmer atmosphere.

Volume of a cube = L³
L = length of the cube side

Volume of a half-cylinder = PI r²h/2
r = radius of the cylinder
h = height of the cylinder

Surface area of a cube = 6L²

Surface area of the half-cylinder = PI r² + dh + PI rh
d = diameter of the cylinder (equal to 2r)
The first term is the area of the two semicircles
The second term is area of the flat rectangle
The third term is the area of the curved rectangle

If you put values into these equations, you will find that the half-moon 
shape ice has greater surface area.  However, the surface area of this 
shape can change if you alter some of the dimensions.

In the worked calculations that I have done, I assumed that each ice shape 
weighed 8g and that ice has a density of 0.917g per cubic centimetre, so 
each ice shape has a volume of about 8.72 cubic centimetres.

As the volume of the cube is L³ = 8.72 cubic centimetres, the cube root of 
8.72 is 2.06, so L = 2.06 cm.  From this, the surface area was found to be 
about 25.46 square centimetres.

For the half-moon (half-cylinder), the volume is PI r²h/2 = 8.72 cubic 
centimetres.  Assuming the height (or thickness) of the half-moon to be 
1cm, r² = 5.55 so by taking the square root of 5.55, the radius may be 
found to be 2.36 cm (hence d = 4.72 cm).  Putting the values into the 
surface area equation gives a result of 29.63 square centimetres.

By using different values of h (say 2 or 3), different values of r are 
generated, which alters the surface area of the half-moon shape.

You could try comparing other shapes by finding the equations for volume 
and surface area, how about how quickly a ball (sphere) of ice melts?  

Check out www.math.com for some formulas.

I hope that this has been of some help to you Jennifer.

Chris Wilson, Research Chemist, Cooper Vision,
Southampton, Hampshire, England.