The volume of the total amount of sugar in the container is 1371 16 cubic inches. The depth of the sugar layer is 834 inches, and the dimensions of the container must multiply to 165 cubic inches.
To determine the volume of the total amount of sugar in the container, we need to find the depth of the sugar layer. Since the height of the container is 12 inches and the current amount of sugar is 134 inches from the top, the depth of the sugar layer is 12 - 134 = 834 inches.
Now, we can calculate the volume of the sugar layer using the formula for the volume of a rectangular prism:
Volume = Length × Width × Height
Assuming the length and width of the container are given, let's say L and W respectively, we can calculate the volume of the sugar layer as:
Volume = L × W × 834
Since the volume is given as 1371 16 cubic inches, we can set up an equation:
1371 16 = L × W × 834
Solving for L × W, we get:
L × W = 1371 16 ÷ 834 = 165
So, the length and width of the container must multiply to 165 cubic inches. This means that the dimensions of the container could be (15, 11), (11, 15), any other combination of factors that multiplies to 165.