Final answer:
The volume of a cone with a height of 5m and a diameter of 12m is 60π cubic meters.
Step-by-step explanation:
To find the volume of a cone with a height of 5m and a diameter of 12m, we use the volume formula for a cone, which is V = (1/3)πr²h, where r is the radius of the base of the cone and h is its height. Since the diameter is given as 12m, the radius (r) is half of that, which is 6m. Substituting these values into the formula gives:
V = (1/3)π(6m)²(5m) = (1/3)π(36m²)(5m) = (1/3)π(180m³) = 60πm³.
Therefore, the volume of the cone is 60π cubic meters.