Answer: The volume of the prism is 4200 cubic units.
Step-by-step explanation:
The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height. For a hexagonal base with a side length of 10, we can divide it into six equilateral triangles with side lengths of 10. Each equilateral triangle has an area of (1/2)bh, where b is the base and h is the height. Since the base of each equilateral triangle is also 10, we have:
Area of one equilateral triangle = (1/2)(10)(10√3/2) = 50√3
Area of the hexagonal base = 6 times the area of one equilateral triangle = 6(50√3) = 300√3
Now we can use the formula for the volume of a prism:
V = Bh = (300√3)(14) = 4200 cubic units.
Therefore, the volume of the prism is 4200 cubic units.