The radius of a circular puddle is growing at a rate of 25 cm/sec.
(a) how fast is its area growing at the instant when the radius is 50 centimeters?
(b) how fast is the area growing at the instant when it equals 64 square centimeters?

Step-by-step explanation:

a)area A=pi r^2

rate of change of area =dA/dt =2 pi r dr/dt

given dr/dt =25 ,r =50

rate of change of area =dA/dt =2 pi *50 *25 =2500pi=7854

area growing 7854 cm2/s

b)area A=pi r^2

rate of change of area =dA/dt =2 pi r dr/dt

given dr/dt =25 ,A =64

pi r^2 =64

=>r =8/√pi

rate of change of area =dA/dt =2 pi *(8/√pi) *25 =400√pi=708.98

area growing 708.98 cm2/s

529 and 531

step-by-step explanation: