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Homework Help: Working out radius of sphere using Mass&Density

  1. May 26, 2012 #1
    1. The problem statement, all variables and given/known data
    Using mass = 2.473x10^23kg and Density = 7.481g/cm^3 work out the radius of said sphere,


    2. Relevant equations

    D=M/V
    4/3∏r^3

    3. The attempt at a solution

    D=M/V
    DV=M
    V=M/D

    Mass = 2.473x10^23kg
    V=2.473x10^23kg / 7.481g/cm^3
    V=2.473x10^23kg / 0.007481kg/cm^3

    V= 3.31x10^24 cm
    V= 3.31x10^22 km

    Vol of sphere = 4/3∏r^3

    3√(3.31x10^22/(4/3∏)) = 19918033Km

    I assume I have a massive problem in my calculations (I think theres a problem where i changed the 7.481g/cm^3 into 0.007481kg/cm^3) but I'm still pretty unsure about that one, since my answer at the end is in kilograms and the units i used when changing the decimal is in cm^3, I think that's my problem but i'm not sure)

    Thanks

    ><

    Tried to change it into kg/km^3 and i got 2.473x10^23kg / 748.1

    then cube-root((3.31x10^20)/(4/3Pi) to get 4291210 km, still unsure =/

    ><

    Changed it :

    (2.473x10^23kg) / (7.481g/cm^3) into

    (2.473 x 10^23kg) / (0.007481kg/cm^3) noting that it is CM(i remembered at the end ;) )

    3.666622109x10^25cm <--- 4/3PiR^3

    divide
    3.666622109x10^25cm by 4/3Pi then
    cuberoot to get:
    206091073.4 CM(!) / 100 to get meters (=)
    2060910.734 M / 1000 to get KM (=)
    2060.910734 KM -
    rounded to 2061km (4.S.F)

    I hope that's right, it seems reasonably accurate,
     
    Last edited: May 26, 2012
  2. jcsd
  3. May 26, 2012 #2
    Check again on units. When you have units like cm^3, if you want to go to km^3, the conversion is not the same as going from cm to km (you can check this by typing "cm^3 to km^3" vs. "cm to km" in google).
     
  4. May 26, 2012 #3
    but then on my calculator i get 2.060910734 x 10^-7 <--- I don't understand if I have a volume of 206091073.4cm^3, how that can turn into a small decimal number for the radius in kilometers, especially when the mass is 2.473x10^23, its nothing like a neutron star, just a regular planet, so i don't really agree =$

    ><

    Google wanted to give me:

    (2.47300 x ((10^23) kg)) / (7.48100 (g / (cm^3))) = 3.30570779 × 10^19 m^3

    so it would be: cube-root( 3.30570779 × 10^19 m^3 / (4/3Pi) )

    to get: 1990942.041meters /1000 =

    1990.942041km, dividing by 1k because it isnt km^3 its km, like you said, radius isnt squared or cubed, just power1
     
    Last edited: May 26, 2012
  5. May 26, 2012 #4
    to convert g/cm3 to kg/m3

    [itex](\frac{7.481g}{cm^3})[/itex]([itex]\frac{1Kg}{1000g}[/itex])([itex]\frac{100cm}{1m}[/itex])([itex]\frac{100cm}{1m}[/itex])([itex]\frac{100cm}{1m}[/itex])
     
  6. May 27, 2012 #5
    I'm sorry but that really doesn't help me solve my problem, I don't understand what you said, I mean all I wanted to do was convert the

    M/D into Kg (top/bottom) and km^3 from cm^3 at the bottom,

    and then just divide by 4/3∏ then 3√ to get my answer in Km's, but it just wasn't happening, any ideas?


    ><

    http://blip.tv/chemteam/converting-between-g-cm3-and-kg-m3-3101296 - but it isn't km^3 just m^3
     
    Last edited: May 27, 2012
  7. May 27, 2012 #6
    I didn't really follow what you did because it's too much work. I was showing you how to convert your density into kg/m3 because it's always better to convert your units first. So just do that and it's a very simple problem.

    It's the same as converting grams/cm to kg/m except since it's cm3 (because it's volume) I need to put the conversion factor (100cm=1m) 3 times so I end up with meters3.

    http://youtu.be/XKCZn5MLKvk

    Why do you want to convert it to km anyway?
     
    Last edited: May 27, 2012
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