A scalar field $(r,,)=r^{2}si{n}^2$ is defined in spherical coordinates. Consider the surface of a hemisphere of radius $R,$ with its base at $z=0.$ Which of the following are correct?

grad$=2rsi{n}^{2}hat(r)+2r^{2}sincoshat().$

The flux of grad$$ through the hemisphere is $8\frac{R^3}{3}.$

The flux of grad$$ through the circular base is $4\frac{R^3}{3}.$

The total flux of grad$$ through the entire closed surface $($hemisphere $+$ base$)$ is $0.$