0.20 mm/s
0.08 mm/s
0.25 mm/s
0.05 mm/s
Correct answer is B
Given: \(\frac{\mathrm d A}{\mathrm d t} = 4 mm^{2}/s\)
\(\frac{\mathrm d A}{\mathrm d t} = (\frac{\mathrm d A}{\mathrm d r})(\frac{\mathrm d r}{\mathrm d t})\)
\(A = \pi r^{2} \implies \frac{\mathrm d A}{\mathrm d r} = 2\pi r\)
\(\implies 4 = 2\pi r \times \frac{\mathrm d r}{\mathrm d t}\)
\(\frac{\mathrm d r}{\mathrm d t} = \frac{4}{2\pi r} = \frac{4 \times 7}{2 \times 22 \times 8}\)
= \(0.07954 mm/s \approxeq 0.08 mm/s\)