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Homework Help: Sphere and radius

  1. Sep 2, 2010 #1
    1. The problem statement, all variables and given/known data
    Two spheres are cut from a certain uniform rock. One has a radius 4.50cm. The mass of the
    other is 5 times greater. Find its radius


    2. Relevant equations
    r1 = 4.50cm
    r2 = ? when mass is 5x greater


    3. The attempt at a solution
    Looking at this problem I first thought of somehow integrating the volume of a sphere
    which is 4/3[tex]\pi[/tex]r3. But then i though i was just thinking too hard. it made more sense for the radius to be 5x the radius as i figure the mass was proportional to the radius.

    so: r2 = 5(4.50cm) = 22.5cm

    however i got this marked wrong as the answer was 7.69 cm. what wasn't I looking at clearly?
     
  2. jcsd
  3. Sep 2, 2010 #2

    berkeman

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    Staff: Mentor

    You started on the right track. Mass is proportional to volume, so the ratio 5 applies to the two radii how?
     
  4. Sep 2, 2010 #3
    well that would be proportional to the mass right? so if r2 is 5x in mass then r1 is 1/5(mass)? set up my equation to isolate r to get the radius...
     
  5. Sep 2, 2010 #4

    berkeman

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    Staff: Mentor

    Mass is proportional to volume. Write the fraction V1/V2 out fully, and that will show you a ratio involving some form of the radii. That's where the 5x comes into play...
     
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