Here's the handy factoid I always carry around in my toolbox:
When the three dimensions of a solid object all change by a factor of ' K ' . . . .
-- the surface area of the object changes by a factor of K²
-- the volume of the object changes by a factor of K³ .
So I guess if the surface area increases by 3, that means each linear dimension increased by √3, and the volume has to increase by (√3)³ .
That's 5.196 times the dog's original volume.
(And so does his weight. The poor thing is staggering around wondering what was in that last bowl of kibble that he inhaled.)