The volume of a right rectangular prism is calculated by multiplying its length, width, and height:
Volume = length * width * height
Given:
Length = 1/2 m
Width = 1/4 m
Height = 5/4 m
Plugging in the values:
Volume = (1/2) * (1/4) * (5/4)
Volume = 5/32
Now, in order to show that the product of the edge lengths of the prism is the same as the volume found by packing the prism with unit cubes, we can find the number of unit cubes needed to fill the prism.
Since the edge length of the unit cubes is 1/4 m, we can calculate the number of unit cubes needed in each dimension:
Number of unit cubes in length = 1/2 / 1/4 = 2
Number of unit cubes in width = 1/4 / 1/4 = 1
Number of unit cubes in height = 5/4 / 1/4 = 5
Therefore, the total number of unit cubes needed to fill the prism = 2 * 1 * 5 = 10
Since each unit cube has a volume of (1/4)^3 = 1/64, the total volume of the prism can also be calculated as:
Volume = 10 * 1/64 = 10/64 = 5/32
Therefore, the volume of the prism is 5/32 cubic meters.
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 1/0 unit cubes with an edge length of 1/4 m. What is the volume of the prism?
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