Question

An advertising balloon has radius 6m. Air leak out at a rate of 28 pi m^3/minute. Find the rate of decrease of the diameter after 9 minute ?

Answer 1

what is the volume of a sphere in term of the radius?

Answer 2

oh i think it is
\[V=\frac{4}{3}\pi r^3\]

Answer 3

taking derivatives you get
\[V'=4\pi r^2 r'\]
you are told \(V'=28\) solve for \(r'\)

Answer 4

ohh

Answer 5

how about 9 min ?

Answer 6

i made an equation like this:
28= 4/3π3r dr/dt

Answer 7

i mean r^2

Answer 8

yes, and you can find \(r\) because you know that initially it was 6 m and you know the rate of decrease

Answer 9

thank you :)