Choose a reference point R in the volume and compute the resultant force and torque at this point, F = ∭ ∭ Q f ( r ) d V = ∭ ∭ Q ρ ρ ( r ) d V ( − − g k ^ ^ ) = − − M g k ^ ^ , and T = ∭ ∭ Q ( r − − R ) × × f ( r ) d V = ∭ ∭ Q ( r − − R ) × × ( − − g ρ ρ ( r ) d V k ^ ^ ) = ( ∭ ∭ Q ρ ρ ( r ) ( r − − R ) d V ) × × ( − − g k ^ ^ ) .