Question

Question

Use the image to answer the question.

An illustration shows a 3 D rectangular cuboid segmented into 5 rows by 2 columns of blocks. The length is start fraction 1 over 2 end fraction, width is start fraction 1 over 4 end fraction, and height is start fraction 5 over 4 end fraction.

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

[AI-generated answer — Bot GPT 3.5]

The volume of a right rectangular prism is calculated by multiplying the length, width, and height. In this case, the volume of the prism is:

Volume = 12 m x 14 m x 54 m = 9072 cubic meters

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, we can calculate the volume of one unit cube and then multiply it by the total number of cubes used to pack the prism.

Volume of one unit cube = 14 m x 14 m x 14 m = 2744 cubic meters

Total volume of 10 unit cubes = 2744 cubic meters x 10 = 27440 cubic meters

Since the two volumes are the same, we have verified that the product of the edge lengths is equal to the volume obtained by packing the prism with unit cubes.