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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.

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  1. UnkleRhaukus
    • one year ago
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    density \(\varrho\), is equal to the mass \(m\), per volume \(V\) \[\varrho = m/V\] Calculate the volume of the cube

  2. anonymous
    • one year ago
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    How do you calculate the volume of the cube?

  3. UnkleRhaukus
    • one year ago
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    the volume \(V\), of a cube is equal to the length of its sides \(s\), cubed. \[V =s^3\]

  4. anonymous
    • one year ago
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    so you would cube the 2.72?

  5. UnkleRhaukus
    • one year ago
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    you are given that the sides are \(s=2.72[\text{cm}]\)

  6. UnkleRhaukus
    • one year ago
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    What volume does this make?

  7. anonymous
    • one year ago
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    If you cube the 2.72 cm?

  8. UnkleRhaukus
    • one year ago
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    yes,

  9. anonymous
    • one year ago
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    20.123648 cm^3

  10. UnkleRhaukus
    • one year ago
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    good, thats the volume, now the density is \[\varrho = m/V = \frac{130[\text g]}{20.123648 [\text{cm}^3]}=\]

  11. anonymous
    • one year ago
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    6.460061317g/cm^3

  12. UnkleRhaukus
    • one year ago
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    yeah thats it, now you might want to round to 3 significant figures, (because the values given are themselves only accurate to 3sig.figs)

  13. anonymous
    • one year ago
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    So 6.460

  14. UnkleRhaukus
    • one year ago
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    (that is four significant figures)

  15. anonymous
    • one year ago
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    Whoops 6.46

  16. UnkleRhaukus
    • one year ago
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    yeah, i would leave my final answer as \(\varrho=6.46\,[\text g/\text{cm}^3]\)

  17. anonymous
    • one year ago
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    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.

  18. UnkleRhaukus
    • one year ago
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    OK, well since the substance is the same, the density (an intrinsic quality) will remain the same

  19. UnkleRhaukus
    • one year ago
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    rearranging\[\varrho=m/V\] we get\[m =\varrho\cdot V\] again the volume of a cube is \(s^3\)

  20. anonymous
    • one year ago
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    7.51^3 = 423.564751

  21. UnkleRhaukus
    • one year ago
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    now multiply that, by the density we found earlier

  22. anonymous
    • one year ago
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    2736.228291

  23. UnkleRhaukus
    • one year ago
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    and what are the units?

  24. anonymous
    • one year ago
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    grams

  25. anonymous
    • one year ago
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    since mass was being calculated for

  26. UnkleRhaukus
    • one year ago
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    yeah, so what is our final answer with units (and to 3sig.figs)

  27. anonymous
    • one year ago
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    Alright and if it wants it in scientific notation would it be 2.73 x 10^3?

  28. UnkleRhaukus
    • one year ago
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    \[2.74 \times 10^3\,[\text g]=2.74\,[\text{kg}]\]

  29. anonymous
    • one year ago
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    Thanks. Didn't notice the 6 there.

  30. anonymous
    • one year ago
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    Thanks for the help!

  31. UnkleRhaukus
    • one year ago
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    notice that the ratio of volumes \(424\,[\text{cm}^3]/20.1\,[\text{cm}^3]\approx21\), is equal to the ratio of masses \(2740\,[\text g]/130\,[\text g]\approx21\)

  32. UnkleRhaukus
    • one year ago
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    (as we should expect for a substance of constant density )

  33. anonymous
    • one year ago
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    I didn't notice that. That's interesting and that does make sense for it to.

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