Suppose that each of the smaller cubes is
1 in. high. The area of one face of the cube is length
times width: 1 x 1 = 1 or 1 sq. in.
On each cube there are six faces, each with
an area of 1 sq. in. The total surface area for each of
the cubes is 6 sq. in. The surface area of the three cubes
is 3 x 6, or 18 sq. in.
The big block of ice has four faces, each
with an area of 3 x 1 for a total of 12 sq. in. The block
has two faces with the surface area of 1 x 1 for a total
of 2 sq. in.
Thus, the surface area of the block of ice
is 12 + 2 or 14 sq. in. The three cubes broken apart will
melt more quickly since the surface area of 18 sq. in.
is exposed while the block of ice has only 14 sq. in.
Think what happens when you cut the block
into cubes. There is more exposed surface area so the
cubes melt faster.