Two girders are made of the same material. Girder A is 3.0 times longer than girder B and has a cross-sectional area that is 1.4 times bigger than girder B. What is the ratio of the density of girder A to the density of girder B?
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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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