A stone is dropped into a quiet lake and waves move in circles at a speed of 5 cm/s. When the radius of the circular wave is 8 cm, how fast is the enclosed area increasing?
A stone is dropped into a quiet lake and waves move in circles at a speed of 5 cm/s. When the radius of the circular wave is 8 cm, how fast is the enclosed area increasing?
- A. 40π cm²/s
- B. 80π cm²/s
- C. 8π cm²/s
- D. 160π cm²/s
Answer: B) 80π cm²/s
Explanation: Given dr/dt = 5. Area A = πr². dA/dt = 2πr(dr/dt). At r = 8, dA/dt = 2π(8)(5) = 80π cm²/s.
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