Multiply the edge lengths of a right rectangular prism with length 12 m, width 14 m, and height 54 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 14 m. What is the volume of the prism?

Answer 1

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

Volume = length x width x height
Volume = 12m x 14m x 54m
Volume = 9072m^3

Now, we can find the volume of the prism by packing it with 10 unit cubes with an edge length of 14m:

Volume = number of cubes x volume of each cube
Volume = 10 cubes x (14m x 14m x 14m)
Volume = 10 cubes x 2744m^3
Volume = 27440m^3

Since both calculations give us the same volume, we can conclude that the product of the edge lengths of the prism is equal to the volume of 10 unit cubes packing the prism. The volume of the prism is 9072m^3.