Final answer:
The volume of the trough can be calculated using the formula V = length x width x height. By solving the equation, we find that the trough has a volume of 9 cubic feet.
Step-by-step explanation:
The volume of the trough can be calculated by multiplying the length, width, and height of the trough. Given that the trough is 12 feet long and 3 feet across the top, we need to find the height that corresponds to the given volume.
Let's assume the height of the trough is 'h' feet. The volume formula for a rectangular prism is V = length × width × height. In this case, the volume is given as 9 cubic feet. So we have the equation 12 × 3 × h = 9.
Simplifying the equation, we have 36h = 9. By dividing both sides of the equation by 36, we find that h = 0.25 feet. Therefore, the trough has a volume of 9 cubic feet (option C).