Хермит, а радиус полусферы известен? Если да, то вот:
mg=integrate (h from 0 to H) ρgh*dS(h) = integrate (α from 0 to arcsin(H/R)) ρgRsin(α)*2π(Rcos(α))*dα = integrate (α from 0 to arcsin(H/R)) ρgR*π*sin(2α)*dα = -0,5πρgRcos(2α) (α from 0 to arcsin(H/R)) = -0,5πρgR ( cos(2arcsin(H/R))-1) = -0,5πρgR ( 1-2(H/R)^2-1) = πρgR(H/R)^2 = πρgH^2/R
H=sqrt(mR/πρg)