Question

The radius of a circular puddle is growing at a rate of 15 cm/s.

Answer 1

A = pi r^2 
dA/dt = 2 pi r dr/dt 

dr/dt = 15 cm/s 

a) r = 30 
dA/dt = 2 pi (30) (15) = 900 pi cm^2/s 

b) 
A = 9 = pi r^2 
r = 3 / sqrt(pi) 
dA/dt = 2 pi( 3/sqrt(pi)) (15) = 90 sqrt(pi) cm^2/s