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Subtraction and division problem: volume of 3 balls in cylinder

  1. Dec 10, 2016 #1
    1. The problem statement, all variables and given/known data

    Three identical balls fit snugly into a cylindrical can: the radius of spheres equals the radius of can, and the balls just touch the bottom and the top of the can,
    If the formula for the volume of a sphere is
    V = 4/3 PI * radius * radius * radius, what fraction of the volume of the can is taken up by the balls?

    2. Relevant equations
    Volume of sphere = 4/3 PI * r * r * r
    Volume of cylinder = PI * r * r * h
    3. The attempt at a solution
    Suppose diameter of each ball is 2 so r = 1.

    Vol of 3 balls = 3 * 4/3 PI * r * r *r = 4 * PI

    Volume of cylinder = PI * r * r * h

    Note h = 6 because 3 balls can fit in the cylinder

    Volume of cylinder = 6 * PI
    volume take up by balls is= 6* PI - 4 * PI = 2 PI

    book is not doing subtraction.,
    Some body please guide me why are we not doing subtraction.

    Zulfi.
     
  2. jcsd
  3. Dec 10, 2016 #2

    berkeman

    User Avatar

    Staff: Mentor

    The question is "what fraction of the volume", so you would use a ratio to get the answer, not a subtraction. :smile:
     
  4. Dec 11, 2016 #3
    Hi,
    Thanks. I was also thinking on those lines but you have removed my confusion.
    Zulfi.
     
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