The load on a $2\mathrm{.}5-$in$.-$diameter hydraulic cylinder increases from $10,000$lb to $15,000$lb$.$ Due to the compressibility of the oil, the piston retracts $0\mathrm{.}01$ in $.$ If the volume of oil

under compression is $10$ in $^(3),$ what is the bulk modulus of the oil in units of psi?

a$.266719$ psi

b$.,178717\backslash$psi

c$.312255$ psi

d$.208524$ psi

e$.277818$ psi