A cylindrical beam carries a compression load P = 3000 kN. To prevent the beam from buckling, this load must be less than a critical load,
Pc = π2El/L2
Where E = Young’s modulus = 200 x 109 N/m2, I = πr4/4 (the area moment of inertia for a cylindrical beam of radius r), and L is the beam length. If the volume of beam V cannot exceed 0.075 m3, find the largest height L that can be utilized and the corresponding radius.