I have the volume equation as
then dv/dx = 0 therefore 510-3/2x^2=0
solving for x gives x= + or - (sqrt340)
when x = +(sqrt340)
(d^2v)/(dx^2)= negative therefore maximum
V=510(sqrt340)-0.5(sqrt340)^3 = 6269 m^3
I am not sure about the last part is it just a case of substituting the max x value obtained into the original volume formula?