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 1/2 m, width 1/4 m, and height 5/4 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 1/4 m. What is the volume of the prism?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the volume of the rectangular prism, we multiply the length, width, and height:

Volume = (1/2) * (1/4) * (5/4)
Volume = 5/32 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 1/4 m, we calculate the volume of each unit cube:

Volume of unit cube = (1/4)^3
Volume of unit cube = 1/64 cubic meters

Since there are 10 unit cubes packed into the rectangular prism, the total volume of the unit cubes is:

Total volume of unit cubes = 10 * (1/64)
Total volume of unit cubes = 10/64
Total volume of unit cubes = 5/32 cubic meters

Therefore, we have shown that the product of the edge lengths of the rectangular prism is the same as the volume found by packing the prism with 10 unit cubes. The volume of the prism is 5/32 cubic meters.