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?

Explain why the Correct Answer
is the only Correct Answer

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the volume of the right rectangular prism with length 12 m, width 14 m, and height 54 m, we simply multiply the three edge lengths together:

Volume = length x width x height
Volume = 12 m x 14 m x 54 m
Volume = 9072 cubic meters

To calculate the volume found by packing the prism with 10 unit cubes with an edge length of 14 m, we need to determine how many unit cubes can fit into the prism. Since the prism has dimensions of 12 m x 14 m x 54 m, we can divide each dimension by the edge length of the unit cube (14 m) to find out how many unit cubes can fit in each dimension:

12 m / 14 m = 0.857 cubes
14 m / 14 m = 1 cube
54 m / 14 m = 3.857 cubes

Multiplying these values together gives us the total number of unit cubes that can fit in the prism:

0.857 x 1 x 3.857 = 3.2868785 cubes

Since we can't fit a fraction of a cube, we round down to the nearest whole number, meaning only 3 unit cubes can fit in the prism.

Therefore, the volume found by packing the prism with 10 unit cubes with an edge length of 14 m is:

Volume = 3 x (14 m)^3
Volume = 3 x 2744 m^3
Volume = 8232 cubic meters

The volume of the prism calculated earlier (9072 cubic meters) is not the same as the volume found by packing the prism with 10 unit cubes (8232 cubic meters). So, the initial statement that the product of the edge lengths of the prism is equal to the volume of the prism packed with unit cubes is incorrect. The volume of the prism is actually 9072 cubic meters.