Narrator: "And what happened, then? Well, in Whoville they say - that the Grinch's small heart grew three sizes that day. And then - the true meaning of Christmas came through, and the Grinch found the strength of *ten* Grinches, plus two!"
First, a Grinch's heart's volume can be approximated by a sphere.
Second, the Grinch's heart went from 1 radius to 4 radiuses (grew three sizes).
Third, the Grinch's external volume and weight remained constant.
Fourth, the Grinch's heart is assumed to have remained the same strength.
Fifth, the Grinch's vascular system can be approximated by a pipeline.
Volume of a sphere = (4/3) x Pi x radius3
So, the Grinch's heart changed on the order of: (1)3 to (4)3
The Grinch's heart's volume is now (4 x 4 x 4) = 64 times what is used to be. The Grinch's heart is first described as two sizes too small, so one can assume that his vascular system is able to handle much more than it does now.
When the big heart tries to pump the blood 64 times as quickly, it will encounter frictional losses at a rate of the velocity squared, so he'll only get 8 times more efficient (8 x 8 = 64).
The higher blood friction will also keep him intrinsically warmer, so less other energy will be used to keep him warm. That, coupled with increased adrenal gland activity and general positive demeanor, makes it perfectly feasible that he now has found the strength of 12 Grinches (ten Grinches, plus two).
link to: grinch tv special quiz (I got 8/10)
link to: cardiomegaly
Paul I'm a doctor in any country that ends in "-stan" Totman
Like Hercules, but doesn't need the ring...
