Math CentralQuandaries & Queries


Question from sm:

What is the mass of a length of 1m of trunk a tree trunk of uniform cross section of area 0.5 sq. m is made of wood of relative density 0.8?


The length of tree trunk has a cross section area of $0.5 m^2$ and a length of $1 m$ so its volume is

\[0.5 \times 1 = 0.5 m^{3}.\]

In many problems the units of the given information gives you an indication as to how to solve the problem. That is true in this problem except that you didn't give the units for the density of the wood. I assume the density of the wood is

\[0.8 \;kg/m^{3}.\]

Thus every cubic meter has a mass of 0.8 kilograms and your length of tree trunk has a volume of one-half a cubic meter.


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