Four copies of an acute scalene triangle \mathcal{T}, one of whose sides has length 3, are joined to form a tetrahedron with volume 4 and surface area 24. Compute the largest possible value for the circumradius of \mathcal{T}.
Four copies of an acute scalene triangle \mathcal{T}, one of whose sides has length 3, are joined to form a tetrahedron with volume 4 and surface area 24. Compute the largest possible value for the circumradius of \mathcal{T}.