1. The area of a regular hexagon of side length is given by

2. Area of a circle is πr² (where r is the radius of circle)

3. Area of cylinder = 2πrl (where l is the height of cylinder)

4. The area each face of hex nut: area of hexagon – area of circular hole = – π3² = 65.26

5. The area of each side: 2mm x 6mm = 12 square mm

6. The area of cylindrical inner hole = 2*π*3*2 = 37.7

7. Therefore the total surface area = (2 x area of face) + (6 x area of each side) + (area of cylindrical inner hole)

= 130.5 sq mm + 72 sq mm + 37.7 sq mm =240.2 sq mm

8. And the volume = Surface area x 2 mm = 480.4 cubic mm