Answer is: option1
\(\frac{1}{8\pi}\)Solution:
We start with the equation for the surface area of a sphere:
\[ A = 4\pi r^2 \]
Differentiating both sides with respect to \( t \):
\[ \frac{dA}{dt} = 8\pi r \frac{dr}{dt} \]
Since it is given that:
\[ \frac{dA}{dt} = \frac{dr}{dt} \]
We substitute this into the equation:
\[ \frac{dr}{dt} = 8\pi r \frac{dr}{dt} \]
Dividing both sides by \( 8\pi r \), we get:
\[ r = \frac{1}{8\pi} \]
Thus, the correct answer is: \( \frac{1}{8\pi} \)