Final answer:
The new height of the grain in the second bin with a base of 9 feet by 9 feet would be 6 feet 2 inches, so the answer is B) 6 feet.
Step-by-step explanation:
The student is asking a volume conservation question that requires determining the new height of grain in a different-sized storage bin when the grain is transferred from the original bin. We first calculate the volume of the grain in the first bin and then use this volume to find the height to which the same volume of grain would reach in the second bin.
Volume Calculation for the First Bin
The first bin's dimensions are 12 feet 8 inches (which is 152 inches) by 8 feet 9 inches (which is 105 inches), and the grain is filled to a height of 4 feet 6 inches (which is 54 inches). To find the volume in cubic inches, we multiply these three dimensions:
V1 = Length × Width × Height = 152 inches × 105 inches × 54 inches = 861,840 cubic inches.
Calculating the New Height
Since the base of the second bin is 9 feet by 9 feet (which is 108 inches by 108 inches), to maintain the same volume, we find the new height (H2) using the volume of the first bin:
V1 = Base Area of second bin × New height (H2)
861,840 cubic inches = 108 inches × 108 inches × H2
H2 = 861,840 cubic inches / (108 inches × 108 inches) = 74 inches
Converting 74 inches to feet, we get 6 feet 2 inches. Therefore, the correct answer is B) 6 feet.