Question 862881
Use the positive x axis for radius and the positive y axis for height.  
{{{V=y*pi*x^2}}}.  The description is of the cross section through the middle of the cylinder.  This cross section uses a circle {{{x^2+y^2=70^2}}}.  You can reform the volume either in terms of x or in terms of y.  


{{{V=y*pi*(70^2-y^2)^2}}}
{{{V=y*pi*(24010000-2*4900y^2+y^4)}}}
{{{highlight_green(V=pi*24010000y-9600*pi*y^3+pi*y^5)}}}
Two choices.  Use a graphing tool or try derivative of V and maybe then resort to a graphing tool.  Where is derivative equal to zero?  Corresponding x?  Corresponding volume?


-unfinished-
potentially posting and keeping unfinished.