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
