I'm having trouble with this question on derivatives.

Question

Carlos is blowing air into a spherical soap bubble at the rate of $7 \mathrm{cm}^3/ \mathrm{sec}$. How fast is the radius of the bubble changing when the radius is $11 \mathrm{cm}$? (Round your answer to four decimal places.) So I THINK what I am trying to solve is $\frac{\mathrm{d}r}{\mathrm{d}t}=\frac{\mathrm{d}}{\mathrm{d}t}\frac{4}{3}\pi \cdot r^3$ Using the formula for volume of a sphere. So differentiating in respect to $t$ I end with $\frac{4}{3}(3\pi \cdot r^2) \cdot \frac{\mathrm{d}v}{\mathrm{d}t}$ After applying the given values I end with $$\frac{\mathrm{d}r}{\mathrm{d}t}=\frac{4}{3}(3\pi \cdot 11^2)*7$$ but the answer is $.0046$ (rounded) and I do not know how to reach that answer. How would I go about reaching that answer, and what am I doing wrong? I already know my notation is probably wrong so That is why I posted the original question to see where I get anything from, thanks in advance for the help!

Answer 1

$$\frac{dV}{dt}=\frac{d}{dt}\left(\frac 43 \pi r^3\right)=4\pi r^2 \frac{dr}{dt}$$ If $\frac{dV}{dt} = 7 \text{cm}^3\text{/sec}$ and $r=11$, then we get $$7=4\pi(11)^2 \frac{dr}{dt}$$