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?
The edge lengths of the given prism are:
Length = 12 m
Width = 14 m
Height = 54 m
Their product is:
12 * 14 * 54 = 9072
To find the volume of the prism using 10 unit cubes with an edge length of 14 m, we need to find how many cubes can fit along each dimension.
The length of the prism is 12 m, so we can fit 12/14 = 0.857 cubes along that dimension. Rounded to the nearest whole number, that's 1 cube.
The width of the prism is 14 m, so we can fit 1 cube along that dimension.
The height of the prism is 54 m, so we can fit 54/14 = 3.857 cubes along that dimension. Rounded to the nearest whole number, that's 4 cubes.
So the total number of cubes that can fit in the prism is 1 * 1 * 4 = 4.
The volume of one unit cube with an edge length of 14 m is:
14 * 14 * 14 = 2744
So the total volume of the 4 cubes is:
4 * 2744 = 10976
This is slightly larger than the volume of the prism calculated using the edge lengths, which was 9072. This is likely due to rounding errors in our calculations.
Therefore, the volume of the prism is approximately 9072 cubic meters.