Question

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? (1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The volume of a right rectangular prism is found by multiplying its length, width, and height.

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

To find the volume by packing the prism with unit cubes, we calculate the number of unit cubes that can fit in the prism.

Number of unit cubes = (length of prism / length of unit cube) x (width of prism / length of unit cube) x (height of prism / length of unit cube)
Number of unit cubes = (12m / 1) x (14m / 1) x (54m / 1)
Number of unit cubes = 12 x 14 x 54
Number of unit cubes = 9072

Since the number of unit cubes is equal to the volume of the prism, the product of the edge lengths is the same as the volume.

So, the volume of the prism is 9072 m^3.