Question 1013226
Cross section through the middle can be a circle and if centered at the Origin for graphing,  {{{x^2+y^2=20^2}}}.


x=r and use r, as if a constant, to find y.


Volume of the cylinder will be {{{2*y*pi*r^2}}};  you'll need the picture to see this.


{{{r^2+y^2=400}}}
{{{y=sqrt(400-r^2)}}}


volume is {{{2pi*sqrt(400-r^2)r^2}}}-----answer

Do not confuse radius of the circle or sphere with the radius of the cylinder.