Multiply the edge lengths of a right rectangular prism with length 1/2 m with 1/4 m in height 5/4 m to show that the product is the same as the volume 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

To find the volume of the prism, we multiply the edge lengths:

Volume = Length x Width x Height
Volume = (1/2) x (1/4) x (5/4)
Volume = 5/32 cubic meters

To pack the prism with 10 unit cubes with an edge length of 1/4 m, we need to find the total volume by adding up the volumes of the unit cubes. The volume of one unit cube is (1/4) x (1/4) x (1/4) = 1/64 cubic meters.

Therefore, the total volume of the prism, when packed with 10 unit cubes, is:

10 x (1/64) = 10/64 = 5/32 cubic meters

This shows that the product of the edge lengths of the prism is the same as the volume of the prism.