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A prisms base is a hexagon of a side length 10 The height of the prism is 14 Find the volume of the prism

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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.

User Tom Hennen
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