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anonymous
 one year ago
Calculate the density of a solid substance if a cube measuring 2.72 cm on one side has a mass of 130g.
anonymous
 one year ago
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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UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2density \(\varrho\), is equal to the mass \(m\), per volume \(V\) \[\varrho = m/V\] Calculate the volume of the cube

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How do you calculate the volume of the cube?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2the volume \(V\), of a cube is equal to the length of its sides \(s\), cubed. \[V =s^3\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so you would cube the 2.72?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2you are given that the sides are \(s=2.72[\text{cm}]\)

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2What volume does this make?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If you cube the 2.72 cm?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2good, thats the volume, now the density is \[\varrho = m/V = \frac{130[\text g]}{20.123648 [\text{cm}^3]}=\]

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2yeah thats it, now you might want to round to 3 significant figures, (because the values given are themselves only accurate to 3sig.figs)

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2(that is four significant figures)

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2yeah, i would leave my final answer as \(\varrho=6.46\,[\text g/\text{cm}^3]\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright 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
 one year ago
Best ResponseYou've already chosen the best response.2OK, well since the substance is the same, the density (an intrinsic quality) will remain the same

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2rearranging\[\varrho=m/V\] we get\[m =\varrho\cdot V\] again the volume of a cube is \(s^3\)

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2now multiply that, by the density we found earlier

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2and what are the units?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0since mass was being calculated for

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2yeah, so what is our final answer with units (and to 3sig.figs)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright and if it wants it in scientific notation would it be 2.73 x 10^3?

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2\[2.74 \times 10^3\,[\text g]=2.74\,[\text{kg}]\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks. Didn't notice the 6 there.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks for the help!

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.2notice 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
 one year ago
Best ResponseYou've already chosen the best response.2(as we should expect for a substance of constant density )

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I didn't notice that. That's interesting and that does make sense for it to.
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