Modelling radius of spherical balloon as it is inflated

[apple2357]

Ok, so i am trying to get my head around this problem we were set.
What would the graph of this situation look like over time? I know i have to make some assumptions to simplify the problem and calculus might help.
So V= 4/3 pi r^3 and dv/dr etc but all i want is a sense of how the radius changes over time.
Any ideas?

 

[lev888]

Show how volume depends on time and radius on volume. Combine, graph.

 

[apple2357]

Ok so, suppose the rate of volume increase is at 1cm cubed per second.
So that is dv/dt i guess. Do i work out dr/dt from that and then sketch?

 

[Dr.Peterson]

Ok, so i am trying to get my head around this problem we were set.
What would the graph of this situation look like over time? I know i have to make some assumptions to simplify the problem and calculus might help.
So V= 4/3 pi r^3 and dv/dr etc but all i want is a sense of how the radius changes over time.
Any ideas?

It will help if you quote the exact, entire problem as given to you, so we can be sure what is expected. You have made it extremely vague.

Yes, you can use calculus to find the rate, if that is the goal. If you want to, please tell us what experience you have with such "related rates" problem, and show an attempt at it based on what you have learned.

But that is not essential for the broad problem as you have stated it. You could simply suppose that the volume is increasing at a constant rate starting from 0; if dimensions are in centimeters and the rate is 1 cm³/sec, then V = t! (In general, V = rt.) So you can just replace V in your volume equation and solve for r to find exactly what the radius is as a function of time.

Furthermore, if a graph is expected, then what I suggested in the last paragraph must be what you are to do, because you can't graph either r or V as a function of time if all you know is the rate at a given moment. You need a function. So that is my recommendation -- if what you wrote reflects the actual problem.

 

[apple2357]

It will help if you quote the exact, entire problem as given to you, so we can be sure what is expected. You have made it extremely vague.

Yes, you can use calculus to find the rate, if that is the goal. If you want to, please tell us what experience you have with such "related rates" problem, and show an attempt at it based on what you have learned.

But that is not essential for the broad problem as you have stated it. You could simply suppose that the volume is increasing at a constant rate starting from 0; if dimensions are in centimeters and the rate is 1 cm³/sec, then V = t! (In general, V = rt.) So you can just replace V in your volume equation and solve for r to find exactly what the radius is as a function of time.

Furthermore, if a graph is expected, then what I suggested in the last paragraph must be what you are to do, because you can't graph either r or V as a function of time if all you know is the rate at a given moment. You need a function. So that is my recommendation -- if what you wrote reflects the actual problem.

The problem is all about making assumptions in the modelling cycle. Its simply, make any assumptions you like, to do a rough sketch of the real life situation.
But i think i am getting there. I am assuming the volume increases at a constant rate of 1 cm cubed per second which tells me V=t so then t= 4/3 pi r^3 so i can rearrange this for r and get a graph which tells me the general shape.

So i think i have got somewhere. Your responses helped and made me think so thanks!