Answer is: option2
10Solution:
Given the area of a circle:
\( A = \pi r^2 \)
Differentiate both sides with respect to \( t \):
\(\frac{dA}{dt} = \frac{d}{dt} (\pi r^2) \)
\(\frac{dA}{dt} = 2\pi r \frac{dr}{dt} \)
Given:
\( r = 5 \) inches
\(\frac{dr}{dt} = \frac{1}{\pi} \) inches per second
\(\frac{dA}{dt} = ? \)
Substituting the given values:
\(\frac{dA}{dt} = 2 \times \pi \times 5 \times \left(\frac{1}{\pi}\right) \)
\(\frac{dA}{dt} = 10 \) square inches per second
Final Answer: 10 inches per second