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One cm^3 of water is 1g. Ant's a lot smaller.

Alternatively, 1mm^3 of water is 1mg. Imagine the average ant as the sum of three balls, each measuring 1mm^3. That's 3mg.

While a sphere is going to be in the same ballpark, a cube of 1mm³ is presumably easier to imagine.

Except an ant looks like 3 spheres

For the purpose of this exercise, assume a rectilinear ant.

The commenter was pointing out that a sphere of volume 1 mm^3 has a diameter of 1.24 mm, while a sphere of diameter 1 mm has a volume of 0.52 mm^3.

Meanwhile a cube of side 1 mm has a volume of 1 mm^3.

Some ants are get pretty sizeable.