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## Homework Equations

Vsphere = (4/3)(π)(r^3)

C = (2)(π)(r)

## The Attempt at a Solution

[/B]My strategy was to come up with two separate equations of dr/dt and substitute leading to an equation relating dv/dt and dc/dt

dV/dt = (4)(π)(r^2) (dr/dt)

dc/dt = (2)(π)(dr/dt)

(dc/dt) (1/2π) = dr/dt

Substitute...

(4)(π)(r^2) (dc/dt) (1/2π) = dv/dt

Canceling like terms

(2r^2)(dc/dt) = dv/dt

(1/2r^2) (dv/dt) = (dc/dt)

Now I was curious and wanted to graph the function just for fun. I know dv/dt is some number so I assumed it is 3. This yields

3/2r^2 = dc/dt

If I were to graph this function on a graphing utility would I be getting the circumference on the y axis and time on the x? I ask this because the function is decreasing but the circumference of the balloon is increasing. Please help.