A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2.1 ft/s.

Question

(a) How rapidly is the area enclosed by the ripple increasing when the radius is 5 feet?

 

 

(b) How rapidly is the area enclosed by the ripple increasing at the end of 9.8 seconds?

Answer 1

These two RATES are RELATED in the equation A = pi r²

 

If you take the derivative of that equation with respect to t, you will have an equation with both your rates.  Solve for dA/dt.