Let us first look at what density means; the density of an
object is the mass of the object divided by the volume of the object. The density of an
object does not change merely by a change in its volume, the change in mass, if any,
also has to be considered.
Here, girder A is 3 times longer
and has a cross-sectional area that is 1.4 times that of girder B. I do not know if by
the way the question is framed you mean that they are made of the same mass of material
or they are just made of the same material. In the latter case, as they are made of same
material, the mass of girder B will increase as its volume increases. There would then
be no change in the density and the ratio of the density of girder A and the density of
girder B is equal to one.
On the other hand, if girder A
and B are made of the same mass of material as the volume of girder A is 3*1.4 = 4.2
times that of girder B, the ratio of the density of girder A to that of girder B would
be 1/4.2.
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