Final answer:
The height of a cone with a volume of 2,016 cubic meters and a base width of 10 meters is calculated using the volume formula for a cone. After calculating, the resulting height is approximately 77.16 meters, which doesn't match any of the provided answer choices.
Step-by-step explanation:
To find the height of the cone given its volume and the width of its base, we can use the formula for the volume of a cone, which is V = (1/3) π r^2 h, where V is the volume, r is the radius of the base, and h is the height of the cone. Since the width of the base is 10 meters, the radius r will be half of that, which is 5 meters. Plugging the values into the formula and solving for h gives us:
- 2,016 m^3 = (1/3) π (5 m)^2 h
- 2,016 m^3 = (1/3) π 25 m^2 h
- 2,016 m^3 = (25/3) π m^2 h
- h = (2,016 m^3) / ((25/3) π m^2)
- h = 2,016 m^3 / (8.333 m^2 π)
- h ≈ 77.16 m
The closest answer to 77.16 meters from the options provided is 64 meters (A), but the exact calculated height is not one of the options. None of the options provided (A, B, C, D) are correct based on this calculation.