that should be dv/dt.
to do part i just integrate both sides of, vdv=1000(2t+1)^(-2) dt
ii) put t=5 into answer part(i) to get V then use V=4/3pi(r)^3 to find r
iii) put t=5 and your answer to part(ii) into your expression for dr/dt which you should have as 1000/[4pi r^2(2t+1)^(2)]