Question 1011918
Make a circle on cartesian system, radius of the circle, 1.
{{{x^2+y^2=1}}}


x will be the radius of the CYLINDER.
The cylinder height will be  {{{y=sqrt(1-x^2)}}}.


That only gives you a figure for the largest cross section; but you want VOLUME, so....



{{{v=y*pi*x^2}}}, because the base radius for the cylinder is x.
Substitute for y.


{{{highlight(v=pi*x^2*sqrt(1-x^2))}}}-----No really - My mistake was to forget accounting for both parts of what make the "height".  This would be 2y, instead of just y.  The tutor iklyen gave the correct answer, result.