Question 1052763
You stated THESE two equations:   {{{system(V=(3-(r^2/3))(h),h/(2-r)=5/2)}}}



Solve the second equation for r in terms of h.
{{{2h=5(2-r)}}}
{{{2h=10-5r}}}
{{{-5r=2h-10}}}
{{{r=-2h/5+2}}}
{{{r=2-2h/5}}}
easier soon  if as  {{{r=2(1-h/5)}}}
{{{r=2(5-h)/5}}}
{{{r=(2/5)(5-h)}}}-----might be easiest to use



Substitute for r in the first equation , formula for V.
{{{V=(3-((2/5)(5-h))^2/3)h}}}
and start simplifying...
{{{V=(3-(4/25)(25-10h+h^2)/3)h}}}
and continue.
{{{V=(3-(4-(40/25)h+(4/25)h)/3)h}}}, not quite done yet...


...the solving steps shown above might not be the most efficient or neat, but the finished answer in most general form seems to be (work done on paper separately),
{{{V(h)=3h-(4/3)h+(8/15)h^2-(4/75)h^3}}}
or finally,
{{{highlight(V(h)=(5/3)h+(8/15)h^2-(4/75)h^3)}}}.