# application of derivatives on concentric circles

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?"

• Hint: what is the area of a circle of radius $r$? – lulu Sep 8 '16 at 15:54
• Is the answer is $2\pi(4)16$=2(4)(16)$\pi$ – Sathasivam K Sep 8 '16 at 16:37

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.