Question

Suppose that a small french bulldog grows isometrically. If its surface area increases by a factor of 3, by what factor does its volume increase by?

Answer 1

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.)