Calculus Problem: Blowing Up a Spherical Balloon

[Idan9988]

Homework Statement

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Relevant Equations

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I'm struggling with section a. This is my calculation:

The expression remains depend on the variable t, while in the answer is a concrete number:

 

[pasmith]

$r = r_0 + 0.9t$ is only valid if $dr/dt$ is constant.

Why did you assume that $dr/dt$ was constant? The question only tells you that $dr/dt = 0.900\,\mathrm{cm}/\mathrm{s}$ when $r = 6.50\,\mathrm{cm}$.

 

[harveysnaf]

Agree,

The answer (a) has all the information. Since the volume flow rate is constant, then $\frac {dV}{dt}$ is a constant.

$\frac {dr}{dt}$ is variable.

If you rearrange the expression to solve for $\frac {dr}{dt}$ and you get the answer to (b) and the behavior that explains (c).

 

[hutchphd]

Calculate $\frac {dV} {dr}$ and use this to inform your answer.