The radius of a circular puddle is growing at a rate of 25 cm/s.

(a) how fast is its area growing at the instant when the radius is 50 cm? hint [see example 1.] (round your answer to the nearest integer.)

(b) how fast is the area growing at the instant when it equals 36 cm2? hint [use the area formula to determine the radius at that instant.] (round your answer to the nearest integer.)

a) 2500π cm/s

b) 300√π cm/s

Step-by-step explanation:

Given:

Rate of growth of radius, = 25 cm/s

Area of circle is given as:

A = πr²

a)Rate of growth of area,

or

⇒ ............(1)

at r = 50 cm

on substituting the respective values, we get

⇒

or

⇒ = 2π(50)25 = 2500π cm/s

b) when area , A = 36 cm²

36 = πr²

r =

thus, using (1)

⇒

on substituting the respective values, we get

⇒

or

⇒ = 300√π cm/s

b

2

−

b

b

3

+

7

b

2

+

14

b

+

6

%

−

3

b

3

+

7

b

2

+

14

b

+

6

%

step-by-step explanation: