Find how fast the circumference of a circl is growing, if its radius $r$ grows according to the following equation:
\[
\frac{d r}{d t}=7 \frac{\mathrm{cm}}{\mathrm{s}}
\]
Show your work here
Answer
\(\boxed{\text{Final Answer: The circumference of the circle is growing at a rate of approximately 43.98 cm/s}}\)
Step 1 ：Given the rate at which the radius is growing: \(\frac{dr}{dt} = 7 \frac{\text{cm}}{\text{s}}\)
Step 2 ：Find the rate at which the circumference is growing: \(\frac{dC}{dt} = 2 * \pi * \frac{dr}{dt}\)
Step 3 ：Plug in the given value: \(\frac{dC}{dt} = 2 * \pi * 7 \frac{\text{cm}}{\text{s}}\)
Step 4 ：Calculate the value of \(\frac{dC}{dt}\): \(\frac{dC}{dt} \approx 43.98 \frac{\text{cm}}{\text{s}}\)
Step 5 ：\(\boxed{\text{Final Answer: The circumference of the circle is growing at a rate of approximately 43.98 cm/s}}\)
