The radius of a circular puddle is growing at a rate of 20 cm/sec. (a) how fast is its area growing at the instant when the radius is 40 centimeters? hint [see example 1.] (round your answer to the nearest integer.) incorrect: your answer is incorrect. cm2/s (b) how fast is the area growing at the instant when it equals 64 square centimeters? hint [use the area formula to determine the radius at that instant.] (round your answer to the nearest integer.)

Part (a)
 The expression for the circle area is given by:
 A = pi * r ^ 2
 Where,
 r: radio
 We now derive the expression of the area with respect to time:
 A '= 2 * pi * r * r'
 Substituting values:
 A '= 2 * pi * (40) * (20)
 A '= 5026.6 cm ^ 2 / s
 
 its area is growing at the instant when the radius is 40 centimeters at:
 A '= 5026.6 cm ^ 2 / s
 Part b)
 A = pi * r ^ 2
 We look for the radio:
 r = root (A / pi)
 r = root (64 / pi)
 r = 4.5 cm
 We now derive the expression of the area with respect to time:
 A '= 2 * pi * r * r'
 Substituting values:
 A '= 2 * pi * (4.5) * (20)
 A '= 565.5 cm ^ 2 / s
 
 its area is growing at:
 A '= 565.5 cm ^ 2 / s