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

Answer:

The ratio of the current volume of the balloon to the original volume of the balloon is:

27: 1