Question

A spherical balloon is being inflated. The radius of the balloon is increasing at the rate of 6 cm/s.

f(t) = 6t

Find a function g that models the volume as a function of the radius r.

g(r) = ?

Answer 1

so r=f(t) then...

Answer 2

what is the formula for the volume of a sphere?

Answer 3

Are you solving this by using derivatives?

Answer 4

Dr/Dt= 6cm/s
V=4/3 π r3
Dv/Dt=4πr^2(Dr/Dt)
Plug in your variables:
Dv/Dt=4πr(6)
So the function would be:
Dv/Dt=24πr