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? (1 point) cubic meters Skip to navigation

Answer 1

To find the volume of a right rectangular prism, you multiply its length, width, and height. Given that the dimensions of the prism are:

• Length = 12 m
• Width = 14 m
• Height = 54 m

The volume \( V \) can be calculated using the formula:

\[ V = \text{Length} \times \text{Width} \times \text{Height} \]

Substituting the values:

\[ V = 12 , \text{m} \times 14 , \text{m} \times 54 , \text{m} \]

Now, calculating step-by-step:

1. \( 12 \times 14 = 168 \)
2. \( 168 \times 54 = 9072 \)

Therefore, the volume of the prism is:

\[ V = 9072 , \text{cubic meters} \]

If you are also considering packing the prism with unit cubes that each have an edge length of 14 m, these cubes would each have a volume of:

\[ \text{Volume of one cube} = 14 , \text{m} \times 14 , \text{m} \times 14 , \text{m} = 2744 , \text{cubic meters} \]

If you pack 10 such cubes, the total volume packed is:

\[ \text{Total volume} = 10 \times 2744 , \text{cubic meters} = 27440 , \text{cubic meters} \]

This seems to align with the problem context rather than the direct volume of the prism.

In conclusion, the volume of the first prism is:

\[ \boxed{9072} , \text{cubic meters} \]