Today in class our teacher gave us a *fun* take home question and normally I'm fine with them except this time (maybe because physical applications is hard for me), it's been wracking my brain, I've looked in my text books and can't seem to find any real help so any help would be very appreciated
The Question
A block of ice in the form of a cube melts in such a way that the block remains cubic. After a time t hours the black is 3cm^3. Initially the cube has edge 4m and after 9 hours the cube has an end of 1m.
i) If the rate of change of volume. Rm^3 is given by R=-k for some constant k>0 show that V=64-7t.
ii) Hence find when the cube has an edge of 2m.
I intergrated (V=64-7t) and got 64t - 7 x(t^2/2). Is this the right approach or am I going about it all wrong? Thanks, Kim