a spherical balloon is inflated at the rate of 4ft^3/min. What is the volume of the balloon when the radius is increasing at the rate of 6in./min?

Question

freethinker · Answer

@shamil98

freethinker · Answer

first, you need to know the general formula for volume of a sphere

freethinker · Answer

please post your worked out solution or attempt or even from the hint I've been provided

anonymous · Answer

v=(4/3)(pie)r^3

anonymous · Answer

givens: dv/dt=4

anonymous · Answer

find: dv/dt when dr/dt=6

freethinker · Answer

start deriving the volume of a sphere 
4/3 pi is a constant so you can just solve 
4/3 pi * dr^3/dt

freethinker · Answer

power rule 
$$nx^{n-1}$$

anonymous · Answer

i just dont understand what number i would use for the radius

freethinker · Answer

4/3 pi * 3r^2 

3 cancels out so you are left with 
4 pi r^2

freethinker · Answer

you derive first, then you use the derivation at the instantaneous rate being asked which is 6 in. per min

anonymous · Answer

okay thank you sm for your help!!! much appreciated

freethinker · Answer

ask again when you get stuck