A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3.5 ft/s. (a) how rapidly is the area enclosed by the ripple increasing when the radius is 5 feet?

(a) The area is given by

... A = π·r²

The rate of change of area is the derivative of this with respect to time.

... dA/dt = π·2r·dr/dt

For the given conditions, this evaluates to

... dA/dt = π·2· (5 ft) · (3.5 ft/s) = 35π ft²/s ≈ 109.96 ft²/s