let
l = number of licks
v = volume of the sphere
s = surface area of the sphere
k = some constant of dissolution
r = radius of sphere

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dv/dl = k*s (the rate of licking is proportional to the current surface area)

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dv/dl = k*(4*pi*r^2) (formula for SA of sphere)
dv/dl = kr^2 (allow constant to "absorb" other constants)

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For volume of sphere:
v = (4/3)*pi*r^3
r = cuberoot((3/4)(1/pi)v)

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dv/dl = k(cuberoot(3/4)(1/pi)v)^2
dv/dl = kv^(2/3) (simplify and absorb constants)

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separate variables
v^(-2/3)dv = k*dl

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integrate
3v^(1/3) = kl+C
l = (3v^(1/3)-C)/k

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Let us use the fact that 0 volume implies 0 licks to get C
0 = (3*0^(1/3)-C)/k
0 = -C/k
C = 0

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so we have
l = (3v^(1/3))/k
l = k*v^(1/3) (absorb constants)

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so the number of licks is proportional to the cuberoot of the volume

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I did the math, you can do the science. You can take a smaller lollipop for instance, find it's volume, see how many licks it takes. That gives you values for l and v that you could plug into the equation to find the value of k. Then to answer your specific question, substitute 113.0973355292326 for the volume and whatever value of k you found for k into the formula and that should spit out the number of licks.

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I'm a bit shaky on my results since the conclusion doesn't seem intuitively correct, but I'll run this by a few professors to verify / disprove my calculations.