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

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.