I assume the area ##S=233pi## is given not circumference.
Then
##V~~4742.12pi##
In terms of given circumference ##C##
##V=C/(6pi^2)##
The formula for volume of a sphere of a radius ##R## is
##V=4/3piR^3##
The formula for area of a sphere of the same radius is
##S=4piR^2##
Given the surface area we can find a radius from the last formula:
##R=sqrt(S/(4pi))= sqrt((233pi)/pi)=sqrt(233)##
Now we can fund volume:
##V=4/3piR^3=4/3pi(sqrt(233))^3~~4742.12pi##
If instead of an area circumference of the equator (the largest circle on a surface of a sphere) is given the calculations are:
##C=2piR##
##R=C/(2pi)##
##V=4/3piR^3=4/3pi(C/(2pi))^3=4/3piC^3/(8pi^3)=C^3/(6pi^2)##