Manuel bought a balloon (that is a perfect sphere) with a radius of 2 \text{ cm}2 cm2, space, c, m. he wanted his balloon to be bigger, so he blew 222 big breaths of air into the balloon. each big breath increased the balloon's radius by 1 \text{ cm}1 cm1, space, c, m. what is the ratio of the current volume of the balloon to the original volume of the balloon?

The original volume of the balloon is given by:
 V1 = (4/3) * (pi) * (r ^ 3)
 Where,
 r: radius of the sphere.
 Substituting values:
 V1 = (4/3) * (pi) * (1 ^ 3)
 V1 = (4/3) * (pi) * (1)
 Then, the volume of the current sphere is:
 V2 = (4/3) * (pi) * ((1 + 2 * (1)) ^ 3)
 V2 = (4/3) * (pi) * ((1 + 2) ^ 3)
 V2 = (4/3) * (pi) * ((3) ^ 3)
 V2 = (4/3) * (pi) * (27)
 The relation of volumes is:
 V2 / V1 = ((4/3) * (pi) * (27)) / ((4/3) * (pi) * (1))
 V2 / V1 = 27/1
 
 The ratio of the current volume of the balloon to the original volume of the balloon is:
 27: 1