Final answer:
The volume of the cone is approximately 376.99 m³.
Step-by-step explanation:
To find the volume of a cone, we can use the formula V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone. In this case, the diameter of the cone is 12 m, so the radius is half of that, which is 6 m. The height of the cone is given as 10 m. Plugging these values into the formula, we get:
V = (1/3)π(6 m)²(10 m)
V = (1/3)π(36 m²)(10 m)
V = (1/3)π(360 m³)
V ≈ 376.99 m³