Final answer:
The volume of water in a cone-shaped tank with a 2 feet water height is found using the formula for the volume of a cone. The radius at 2 feet height is half of the tank's full radius resulting in a volume of 6π cubic feet, therefore, the correct answer is A. 6π cu ft. Therefore, the correct answer is A. 6π cu ft.
Step-by-step explanation:
The volume of water in the tank when the water height is 2 feet can be calculated using the formula for the volume of a cone, which is V = (1/3)πr2h, where r is the radius and h is the height. Because we have a similar smaller cone when the water is at 2 feet, we need to find the scale factor and apply it to the radius before we can find the volume. The scale factor is the ratio of the water height to the full height of the tank, which is 2/4 or 1/2. The diameter of the base of the cone is 12 feet, so the full radius is 6 feet, and for the smaller volume of water at a 2 feet height, the radius will be 3 feet (half of the full radius).
Using the volume formula, the volume of the water in the tank at a 2 feet height is calculated as:
V = (1/3)π(3 ft)2(2 ft)
= (1/3)π(9 ft2)(2 ft)
= (1/3)π(18 ft3)
= 6π ft3
Therefore, the correct answer is A. 6π cu ft.