Question 150283
1) For the Volume of lollipop ----> direct substitution, with given {{{radius=12mmm}}};
{{{V=(4/3)(pi)r^3}}} = {{{(4/3)(pi)12^3}}}
{{{V=7238.823mm^3}}}
2) Since {{{1lick/5 seconds}}} for every {{{40mm^3}}}
By Ratio & Proportion,
{{{7238.823/40}}}={{{1Lick/5seconds}}}
{{{181=1Lick/5seconds}}}
There you go, you need to take 181 licks to finish the whole lollipop.
If you cross multiply, you get the {{{time}}} to finish it,
{{{181*5=905 seconds=15.08minutes}}}
3) If there's a gum in the center w/ radius 5mm:
To get to the center, we subtract this radius from the radius of the lollipop and mark as {{{R[1]}}} to be used.
={{{12-5=7mm=R[1]}}} --> used to get the new volume 
For the Volume= {{{(4/3)(pi)(7^3)}}}={{{1436.755mm^3}}}
Again by Ratio & Prop.
{{{1436.755/40}}}={{{1Lick/5 seconds}}}={{{35.92>=36Licks}}} before you get to the center where the gum is.
Again, you cross multiply for the time frame,
{{{36*5=180seconds=3minutes}}}
Thank you,
Jojo