Ripple on a pond

EasyCalculus~3m

A pebble dropped into a still pond creates a circular ripple whose radius grows at a constant 22 feet per second. At the instant 1010 seconds after the drop, how fast is the enclosed area increasing? Give the value in square feet per second to two decimal places.

Show hints (2)+
  1. Start from A=πr2A = \pi r^2 and differentiate in time: dA/dt=2πr(dr/dt)dA/dt = 2\pi r\,(dr/dt).
  2. Find the radius at t=10t = 10 s first, then plug in dr/dt=2dr/dt = 2.

Answer

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251.33 (± 0.05)

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Asked at: Optiver, DRW

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