Question

A spherical bath oil capsule dissolves in the bath so that its decrease in volume is proportional to its surface area. If its shape remains spherical as it dissolves, show that the radius of the capsule will decrease at a constant rate.

Thanks to anyone who helps

Answer 1

dv/dt = kA
v = 4/3 pi r^3
dv/dt = 4pi r^2 dr/dt = A dr/dt
so, k = dr/dt