An illustration shows a 3 D rectangular cuboid segmented into 5 rows by 2 columns of blocks. The length 1/2 the width is 1/4 and the height is 5/4
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?
The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
Given that:
l = 1/2 m
w = 1/4 m
h = 5/4 m
Multiplying the edge lengths:
(1/2) * (1/4) * (5/4) = 5/64
Thus, the volume of the prism is 5/64 cubic meters.
Now, to show that this is the same as packing the prism with 10 unit cubes with an edge length of 1/4 m:
Each unit cube has a volume of (1/4) * (1/4) * (1/4) = 1/64 cubic meters.
And since there are 10 unit cubes, the total volume of the prism when packed is 10 * 1/64 = 10/64 = 5/32 cubic meters.
Therefore, the volume of the prism found by multiplying the edge lengths is the same as the volume found by packing the prism with unit cubes, both equal to 5/64 cubic meters.