Manuel bought a balloon (that is a perfect sphere) with a radius of 2 cm. he wanted his balloon to be bigger, so he blew 2 big breaths of air into the balloon. each big breath increased the balloon's radius by 1 cm.

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.

true

explanation:

step-by-step explanation: