1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Working out radius of sphere using Mass&Density
  1. Mass density of a sphere (Replies: 14)

Loading...