Geometry

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4 balls each with a radius 1 inch fit snuggly into a 2x2x8 inch box. Is the total volume left over inside the box greater than or less than the volume of a fifth ball? Justify answer.

I got as far as figuring the volume of box is 32 cubic inches

I'm not sure about the balls?

  • Geometry -

    Volume of 1 ball, of radius r
    V=4πr^3/3
    =4π1^3/3
    =4π/3

    Interstitial volume (empty space)
    = 32 in.³ - 4V

    You will find that the volume left over is just slightly less than half the volume of the box.

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