Calculus question

Question

A pebble is dropped into a still pond, causing ripples in the form of concentric circles. The radius r of the outer circle is increasing at a rate of 25cm/s. When the radius is 100cm, at what rate is the total area of the disturbed water increasing?

 

Help!?

Answer 1

Area = A = pi * radius^2

dA/dR = 2*pi*r

dA = 2*pi*r*dR

dA = 2 * pi * 100 * 25

= 5000*pi

Answer 2

A = πr²

 

A(t) = πr(t)²

 

dA/dt = 2πrdr/dt

 

dr/dt = 25 cm/s

 

At r = 100 cm, 

 

dA/dt = 2π (100 cm) (25 cm/s) = 5000π cm²/s ≅ 15708 cm²/s