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a ball has a volume of 45. the radius of the larger ball is 3 times the small ball what is the volume?

  • math -

    Assume the smaller ball has a volume of 45.

    Since volume is proportional to r^3, and R = 3r, the larger V is 3^3 as big as the smaller v, or 27*45 = 1215.

    for the details, see below

    for the smaller ball, v = kr^3 with k=4pi/3

    The larger ball with radius R=3r has volume

    V = kR^3 = k(3r)^3 = 27kr^3 = 27v = 27*45 = 1215

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