Physics Question

Question

Edmund is filling up some water balloons for a party. He managed to buy two types of balloons,

small spherical balloons and larger spherical balloons. From his best guess, he’d say that the radius of

the filled big balloons is triple that of the full smaller balloons. When he starts filling them up, filling up

the larger balloons takes a significantly longer time than the small ones using the same faucet, much

more than triple the time of the smaller balloons. Can you give an explanation to Edmund as to why he

is observing this particular phenomenon? Explain your reasoning.

Answer 1

Hi Kelsey R., the volume of a sphere grows exponentially for radii by the power of 3. (4/3)*π*r³ is the formula. Pour Edmund (ha ha) doesn't realize that an increase in radius by 3 times, increases the volume by 27 (3^3) not 3. You can show this mathematically by setting the ratio of volumes equal to some constant (c) , V2/V1 = C. We'll use R for the radius of the small balloon and 3*R for the radius of the large balloon.

(4/3)*π*(3*R)³ / (4/3)*π*R³ = C, (the volume ratio of the large balloon to the small balloon equals a constant)

27*R³ /R³ = C

C = 27

Thus the large balloon has 27 times the volume of the small balloon.