The volume of a pyramid is 1/3Ah, where A is the base area and h the vertical height. To find the vertical height from the slant height and side length, we need to look at the base in more detail. A regular hexagon consists of 6 equilateral triangles. Six vertices meet at the centre of the hexagon and the "radius" of the hexagon has a length equal to the hexagon side=16. The slant, base and height form a right-angled triangle with hypotenuse 20 (slant), base 16 (radius of the hexagon). The vertical height is sqrt(20^2-16^2)=sqrt(4*36)=2*6=12.
The area of one equilateral triangle is twice the area of a right-angled triangle with hypotenuse=16 and base=8 (a half side length). The height of this triangle is sqrt(16^2-8^2)=8sqrt(3), the triangle area=(1/2)base*height=4*8sqrt(3), the base area is 6*4*8sqrt(3). The area of the equilateral triangle is twice this, 384sqrt(3). The volume is (1/3)384sqrt(3)*12=1536sqrt(3)=2660.43cc.