Suppose a (magical?) ice cube melts, and as it melts
it remains in the shape of a perfect cube, of side length x, and the rate of change in its volume is proportional to its surface area, meaning dvolume/dt=k⋅(surface area).
Initially at time t=0, we have that x is 3 centimeters, but when t=25 minutes, so the cube has been melting for 25 minutes, then x is 2 centimeters. At what time t will I find that x is 1 centimeter?

Question

Suppose a (magical?) ice cube melts, and as it melts
it remains in the shape of a perfect cube, of side length x, and the rate of change in its volume is proportional to its surface area, meaning dvolume/dt=k⋅(surface area).
Initially at time t=0, we have that x is 3 centimeters, but when t=25 minutes, so the cube has been melting for 25 minutes, then x is 2 centimeters. At what time t will I find that x is 1 centimeter?

anonymous · Answer

I got 50 sec ... is this correct ?

anonymous · Answer

Maybe, did you substitute everything?

anonymous · Answer

I think so ... could you show me a solution ?

anonymous · Answer

yeah, its 50 minutes

anonymous · Answer

would love to see your solution ...

anonymous · Answer

I don't know the solution, but i think it is 50. common sense haha

anonymous · Answer

this is a calculus problem ...

anonymous · Answer

I'm aware of that, i just don't know the steps to solving this problem...sry mate

anonymous · Answer

no problem ...

anonymous · Answer

please i am encountering a problem solving this problem, can someone please list a dtep by step procedure which succesfully matches me to the solution ie 50