Question 1197132
Recommend Graphing V =  231r - (pi/2)r^3 as a check for r = 7cm  when Volume is at its Maximum
Obvious max is reached at 7cm (to nearest whole number)
www.padowan.dk/download has an excellent graphing capabilities.

Graphing y = 231x - (pi/2)x^3    (y the volume, x the radius of the Cylinder)
{{{drawing(300,300,  -10,12,-100,1500,   grid(1), blue(line(2.5,6,2.5,-6)) ,
circle(0, -1,0.3),
circle(2, 4, 0.3),
circle(0,0, 0.3),
circle(0,0, 0.3),
graph( 300, 300, -10,12,-100,1500,  0, 231x - (pi/2)x^3)) }}}