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The volume of a spherical balloon is increasing at a rate of $3$ cubic inches per second. After you find the rate of change of the balloon's radius at the time when the radius is $8$ inches explain why this rate is not constant.

I found $dr/dt$ to equal $(3/4)\pi r^2$ but why can't $dr/dt$ be constant?

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$\dfrac 3 4 \pi r^2$ is not constant because it changes are $r$ changes, and thus changes as $t$ changes.

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Since $V=\frac{4}{3}\pi r^3$, we have $\frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$. Notice if $\frac{dr}{dt}$ is constant, then $\frac{dV}{dt}$ is not (it will depend on $r$). However, we're told in the problem that $\frac{dV}{dt}$ is constant.

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