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?

Answer 1

Edge lengths of the right rectangular prism:
Length = 1/2 m
Width = 1/4 m
Height = 5/4 m

Product of edge lengths:
(1/2) * (1/4) * (5/4) = 5/64

Volume of prism by packing with unit cubes:
10 cubes with edge length 1/4 m
Volume = 10 * (1/4)^3 = 10 * 1/64 = 10/64 = 5/32

Therefore, the product of the edge lengths and the volume found by packing the prism with unit cubes is the same, both equal to 5/64. The volume of the prism is 5/32 cubic meters.