Answer:
I guess we want to evaluate how much the volume of the balloon changes in each blow.
The volume of a sphere can be written as:
v = (4/3)*pi*r^3
where pi = 3.1416 and r is the radius of the sphere.
we have that initially, the radius of the sphere is r = 2cm
then v0 = (4/3)*3.1416*(2cm)^3 = 33.5 cm^3
now, after one blow, the radius is 3 cm, so we have:
v1 = (4/3)*3.1416*(3cm)^3 = 113.1cm^3
this means that the change in volume is
v1 - v0 = 97.6cm^3
and after the other blow, we have that the radius is 4cm:
v2 = (4/3)*3.1416*(4cm)^3 = 268.1cm^3
the change in the volume is:
v2 - v1 = 154.9 cm^3
So we can see that the change of 1cm in the radius has a bigger impact if the initial radius of the sphere is bigger.
