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)##