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? (in cubic meters)
To find the volume of the prism, we can use the formula:
Volume = length x width x height
Given:
Length = 1/2 m
Width = 1/4 m
Height = 5/4 m
Volume = (1/2) x (1/4) x (5/4)
Volume = 5/32 cubic meters
Now, let's calculate the volume by packing the prism with 10 unit cubes with an edge length of 1/4 m.
Each unit cube has a volume of (1/4)^3 = 1/64 cubic meters
Total volume of 10 unit cubes = 10 * (1/64) = 10/64 = 5/32 cubic meters
Therefore, the product of the edge lengths of the prism and the volume found by packing the prism with 10 unit cubes is the same, which confirms that the volume of the prism is 5/32 cubic meters.