Calculate the density of a solid substance if a cube measuring 2.72 cm on one side has a mass of 130g.

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Calculate the density of a solid substance if a cube measuring 2.72 cm on one side has a mass of 130g.

Mathematics
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density \(\varrho\), is equal to the mass \(m\), per volume \(V\) \[\varrho = m/V\] Calculate the volume of the cube
How do you calculate the volume of the cube?
the volume \(V\), of a cube is equal to the length of its sides \(s\), cubed. \[V =s^3\]

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Other answers:

so you would cube the 2.72?
you are given that the sides are \(s=2.72[\text{cm}]\)
What volume does this make?
If you cube the 2.72 cm?
yes,
20.123648 cm^3
good, thats the volume, now the density is \[\varrho = m/V = \frac{130[\text g]}{20.123648 [\text{cm}^3]}=\]
6.460061317g/cm^3
yeah thats it, now you might want to round to 3 significant figures, (because the values given are themselves only accurate to 3sig.figs)
So 6.460
(that is four significant figures)
Whoops 6.46
yeah, i would leave my final answer as \(\varrho=6.46\,[\text g/\text{cm}^3]\)
Alright thank you. There is another question like it wanting to calculate the mass of a cube of the same substance measuring 7.51cm on one side.
OK, well since the substance is the same, the density (an intrinsic quality) will remain the same
rearranging\[\varrho=m/V\] we get\[m =\varrho\cdot V\] again the volume of a cube is \(s^3\)
7.51^3 = 423.564751
now multiply that, by the density we found earlier
2736.228291
and what are the units?
grams
since mass was being calculated for
yeah, so what is our final answer with units (and to 3sig.figs)
Alright and if it wants it in scientific notation would it be 2.73 x 10^3?
\[2.74 \times 10^3\,[\text g]=2.74\,[\text{kg}]\]
Thanks. Didn't notice the 6 there.
Thanks for the help!
notice that the ratio of volumes \(424\,[\text{cm}^3]/20.1\,[\text{cm}^3]\approx21\), is equal to the ratio of masses \(2740\,[\text g]/130\,[\text g]\approx21\)
(as we should expect for a substance of constant density )
I didn't notice that. That's interesting and that does make sense for it to.

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