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An illustration shows a 3 D rectangular cuboid segmented into 5 rows by 2 columns of blocks. The length is startfraction 1 over 2 end fraction, width is startfraction 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 1//2 m, width 1/4 m, and height 5/4 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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To find the volume of the prism, we multiply the lengths of the edges:
Volume = length x width x height
Volume = 1/2 x 1/4 x 5/4
Volume = 5/32 cubic meters
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 1/4 m, we can calculate the volume of the unit cubes:
Volume of one unit cube = 1/4 x 1/4 x 1/4 = 1/64 cubic meters
Since the prism can be packed with 10 unit cubes, the total volume from the packing is:
10 x 1/64 = 10/64 = 5/32 cubic meters
Therefore, we have shown that the product of the edge lengths of the prism is the same as the volume found by packing it with unit cubes. The volume of the prism is 5/32 cubic meters.