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 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 1/4 m. What is the volume of the prism?
(1 point)
cubic meters
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To find the volume of the rectangular prism, we multiply the length, width, and height:
Volume = (1/2 m) * (1/4 m) * (5/4 m) = 5/32 cubic meters
To check that this is equal to the volume found by packing the prism with 10 unit cubes, we calculate the volume of each unit cube:
Volume of each unit cube = (1/4 m) * (1/4 m) * (1/4 m) = 1/64 cubic meters
Then, we multiply this by the total number of unit cubes (10):
Total volume of unit cubes = (1/64 cubic meters/cube) * 10 cubes = 10/64 cubic meters = 5/32 cubic meters
Since the result is the same as the volume of the rectangular prism, we have confirmed that the calculation is correct. The volume of the prism is 5/32 cubic meters.