Question

A balloon is expanded to the same volume as that of a human head. Do an order-of-magnitude estimate of the volume of this balloon in cm^3

a. 100cm^3

b. 1,000,000cm^3

c. 10cm^3

d. 1,000cm^3

Answer 1

Volume of balloon = 1000 cm^3

Step-by-step explanation:

The head of a normal person can be assumed as a sphere with radius 10 cm.

Volume of sphere
`=(4)/(3) \pi r^3`, where r is the radius.

We have approximate radius = 10 cm.

Approximate volume of head
`=(4)/(3) \pi r^3=(4)/(3) *\pi* 10^3=4188cm^3`

In the given options the closest value to the approximate volume is 1000 cm^3.

So, volume of head = Volume of balloon = 1000 cm^3