A design on the surface of a balloon is 4 cm wide when the balloon holds 53 cm3 of air. how much air does the balloon hold when the design is 16 cm wide?

Question

A design on the surface of a balloon is 4 cm wide when the balloon holds 53 cm3 of air.  how much air does the balloon hold when the design is 16 cm wide?

anonymous · Answer

Since the lengths increased four times, the volume contained increased (4^3=64) times, assuming the balloon stretches equally in all direction. That's 53*16=846 cm3 of air. source: http://answers.yahoo.com/question/index?qid=20120315042613AADVaC5

anonymous · Answer

Let's assume that we're measuring on a great circle of the balloon (and assume that it's spherical).  Then the 4-fold stretching reflects a 4-fold increase in the perimeter, which is directly proportional to r.  So @maariee is correct that the relative increase in volume is 4^3.

anonymous · Answer

I think there may be a problem with the arithmetic though.