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

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

Product of the edge lengths:
(1/2) * (1/4) * (5/4) = 5/32 m^3

Now, let's calculate the volume found 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 m^3

Volume of 10 unit cubes: 10 * (1/64) = 10/64 = 5/32 m^3

Since the product of the edge lengths and the volume found by packing the prism with unit cubes is the same, the volume of the prism is 5/32 m^3.

Answer 2

in cubic meters