A store owner is packing small radios into larger boxes...

It's correct to divide the total volume of the container by the volume of each radio when you're sure the radios will fit perfectly in the box. They will in this question, because each dimension of a radio is a divisor of a respective dimension of the box (7 is a factor of 42, 5 of 25, and 6 of 60). So we can fit radios in the box so we use the entirety of the box's volume.

If instead we had 7 by 6 by 5 radios, and wanted to put them in a box measuring 1 by 1 by 63000, it would no longer be correct to divide the box volume by the radio volume. In this case, one radio is too long and too wide to even fit in the box, so you couldn't put a single radio into the box, even though this box has the same volume as the one in the question above.