Question

Manuel bought a balloon (that is a perfect sphere) with a radius of 2cm. 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 1cm What is the ratio of the current volume of the balloon to the original volume of the balloon?

Answer 1

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

27: 1

Explanation:

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