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An illustration shows a 3 D rectangular cuboid segmented into 5 rows by 2 columns of blocks. The length is start fraction 1 over 2 end fraction, width is start fraction 1 over 4 end fraction, and height is start fraction 5 over 4 end fraction.
Multiply the edge lengths of a right rectangular prism with length 12 m, width 14 m, and height 54 m to show that the product is the same as the volume found by packing the prism with 10 unit cubes with an edge length of 14 m. What is the volume of the prism?
(1 point)
cubic meters
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First, calculate the volume of the rectangular prism using the given dimensions:
Volume = length x width x height
Volume = 12m x 14m x 54m
Volume = 9072 cubic meters
Next, determine the volume of the 10 unit cubes with an edge length of 1m packed into the prism:
Volume of 1 cube = 1m x 1m x 1m = 1 cubic meter
Total volume of 10 cubes = 10 cubic meters
Since each edge length of the unit cubes is 14m, the total volume of the 10 cubes packed into the prism is:
Volume = 10 x 14 cubic meters = 140 cubic meters
Therefore, the product of the edge lengths of the rectangular prism is equal to the volume found by packing the prism with the unit cubes, as shown:
9072 cubic meters = 140 cubic meters
So, the volume of the rectangular prism is 9072 cubic meters.