the side of the cubes are increasing at the rate of 0.4cm per second. find:

1.the rate the volume increases

2.the rate the surface area is increasing when sides are 10cm

here's how i went about it.

v=s^3 where v is volume, s is length of the side

dv/dt = 3s^2 (ds/dt)

so from the question, the sides are increasing at a rate of 0.4cm per second.

from that you can get ds/dt i think. so how would i write that as ds/dt?

i'm guessing ds/dt = 1.04s as it increases by 4% persecond if the side was intially 1cm but i have no idea how to write ds/dt generally,

if i solve the first question then i'm pretty sure i can do part two.

thanks in advanced for any help