Good day! Is Pythagorean theorem has something to do with this problem? I'm a little bit confuse... any help? "A stone is dropped into a still pond. Concentric circles ripples spread out and the radius of the disturbed region increases at the rate of 16 cm/sec. At what rate does the area of the disturbed region increase when the radius is 4 cm?"
This is an implicit differentiation problem. Let $A$ be the area of the disturbed region and $r$ be the radius of the disturbed region both of which are functions of time. Now we have the relationship $$A(t)=\pi (r(t)) ^ 2.$$ Differentiate both sides with respect to $t$ using the chain rule for the right hand side and substitute the given information.