Answer :
the statement tells you:
dm/dt = k A = 4 pi k r^2 where k is a constant, and r is the radius of the raindrop
use the chain rule to write:
dm/dt = dm/dr x dr/dt
since the raindrop is a sphere (of presumably uniform density), its mass is
m= density x volume = rho x 4 pi r^3/3 where rho is the density of water
so, we have that dm/dr = 4 rho pi r^2, subbing this back we get
dm/dt = 4 pi k r^2 = 4 rho pi r^2 dr/dt
the r^2 on both sides cancel, leaving dr/dt, the rate at which the radius increases, to be constant
dm/dt = k A = 4 pi k r^2 where k is a constant, and r is the radius of the raindrop
use the chain rule to write:
dm/dt = dm/dr x dr/dt
since the raindrop is a sphere (of presumably uniform density), its mass is
m= density x volume = rho x 4 pi r^3/3 where rho is the density of water
so, we have that dm/dr = 4 rho pi r^2, subbing this back we get
dm/dt = 4 pi k r^2 = 4 rho pi r^2 dr/dt
the r^2 on both sides cancel, leaving dr/dt, the rate at which the radius increases, to be constant