Ripple on a pond

EasyCalculus~3m

A pebble dropped into a still pond creates a circular ripple whose radius grows at a constant $2$ feet per second. At the instant $10$ seconds after the drop, how fast is the enclosed area increasing? Give the value in square feet per second to two decimal places.

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

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251.33 (± 0.05)

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Ripple on a pond

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