Question about finding the volume of a Sphere to a certain point 
I've done a few things but I cant seem to figure out how to solve this. Any help please?

Area=$pi(r)^2$
Area=$pi(2Ry-y^2)$
integral of Area from $y=0$ to $y=R/3$ =Volume.
$R=sqrt((R-y)^2+r^2)$
$R^2=(R-y)^2+r^2$
$R^2=R^2-2Ry+y^2+r^2$
$2Ry-y^2+r^2$
$r=sqrt(2Ry-y^2)$
integral of $pi(2Ry-y^2)dy$ from $0$ to $R/3 = pi(Ry)^2-y^3/3$ from $0$ to $R/3$
after plugging in, your answer should be $pi((R(R/3))^2-(R/3)^3/3)$. I hope this was helpful!!
