anonymous
  • anonymous
Calculate the density of a solid substance if a cube measuring 2.72 cm on one side has a mass of 130g.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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UnkleRhaukus
  • UnkleRhaukus
density \(\varrho\), is equal to the mass \(m\), per volume \(V\) \[\varrho = m/V\] Calculate the volume of the cube
anonymous
  • anonymous
How do you calculate the volume of the cube?
UnkleRhaukus
  • UnkleRhaukus
the volume \(V\), of a cube is equal to the length of its sides \(s\), cubed. \[V =s^3\]

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

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