The dimensions of a rectangular prism are Length 2/14 feet width 1 foot Height 1 1/4 feet. The length of the sides of a small cube are 1/4 foot each. Part A. How many small cubes can be packed in the rectangular prism? Part B. Use the answer obtained in Part A to find the volume of the rectangular prism in terms of the small cube and a unit cube.
There are 4 cubes per foot, so in terms of cubes, the prism is
8/14 x 4 x 5
Since you want whole cubes you are out of luck, since 2/14 < 1/4, the size of a cube.
I suspect a typo. Fix it and then apply the logic.
ducc
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Part A. To find out how many small cubes can be packed in the rectangular prism, we need to calculate the number of cubes that can fit along each dimension.
First, let's find the number of cubes that can fit along the length of the rectangular prism. The length of the rectangular prism is 2/14 feet, and the length of each small cube is 1/4 foot. To find out how many cubes fit, we divide the length of the prism by the length of each cube:
Number of cubes along the length = (Length of the prism) / (Length of each cube)
Number of cubes along the length = (2/14) / (1/4)
Number of cubes along the length = (2/14) * (4/1)
Number of cubes along the length = 8/14
Number of cubes along the length = 4/7
Next, let's find the number of cubes that can fit along the width of the rectangular prism. The width of the rectangular prism is 1 foot, and the length of each small cube is 1/4 foot. To find out how many cubes fit, we divide the width of the prism by the length of each cube:
Number of cubes along the width = (Width of the prism) / (Length of each cube)
Number of cubes along the width = 1 / (1/4)
Number of cubes along the width = 1 * (4/1)
Number of cubes along the width = 4
Finally, let's find the number of cubes that can fit along the height of the rectangular prism. The height of the rectangular prism is 1 1/4 feet, and the length of each small cube is 1/4 foot. To find out how many cubes fit, we divide the height of the prism by the length of each cube:
Number of cubes along the height = (Height of the prism) / (Length of each cube)
Number of cubes along the height = (5/4) / (1/4)
Number of cubes along the height = (5/4) * (4/1)
Number of cubes along the height = 5
Now, to find the total number of cubes that can be packed in the rectangular prism, we multiply the number of cubes along each dimension:
Total number of cubes = (Number of cubes along the length) * (Number of cubes along the width) * (Number of cubes along the height)
Total number of cubes = (4/7) * 4 * 5
Total number of cubes = 80/7
Total number of cubes ≈ 11.43
Therefore, approximately 11 cubes can be packed in the rectangular prism.
Part B. Now that we know the number of cubes that can be packed in the rectangular prism is approximately 11, we can use this information to find the volume of the rectangular prism in terms of the small cube and a unit cube.
The volume of a rectangular prism can be found by multiplying its length, width, and height. Let's denote the volume of the rectangular prism as V, the volume of each small cube as v, and the volume of a unit cube as u.
V = (Number of small cubes) * (Volume of each small cube)
V = (Number of small cubes) * v
From Part A, we know that the number of small cubes is approximately 11, so we can substitute this value into the equation:
V = 11 * v
Now, since each small cube has the same volume as a unit cube (v = u), we can further simplify the equation:
V = 11 * v
V = 11 * u
Therefore, the volume of the rectangular prism in terms of the small cube and a unit cube is 11 times the volume of a unit cube.