Related rates of change

Question

a circular ink-blog is formed by ink dripping from a pen onto some blotting paper. The radius of the ink blot is increasing at the rate of 0.3mm/s. Find the rate at which the area of the ink blot is increasing after 3 seconds

 

Answer 1

Let r = radius (in mm) of the inkblot in t seconds

     A = area (in mm²) of the inkblot in t seconds

 

Given:  dr/dt = 3   Find:  dA/dt when t = 3

 

Solution:  A = πr²

 

             dA/dt = 2πr(dr/dt) = 2π(3 mm)(3 mm/sec)

 

                                         = 18π mm² / sec