A box 2m by 4m by 8m is filled with cubes of volume 8cm cubed. If these cubes were lined up , how long would that line be?
To find the length of the line formed by the cubes, we need to calculate the number of cubes that can be arranged in each dimension and multiply by the length of each dimension.
The length of the line formed by the cubes in the 2m dimension can be found by dividing the length of the dimension by the length of each cube:
2m ÷ 0.08m = 25 cubes in the 2m dimension
The length of the line formed by the cubes in the 4m dimension can be found by dividing the length of the dimension by the length of each cube:
4m ÷ 0.08m = 50 cubes in the 4m dimension
The length of the line formed by the cubes in the 8m dimension can be found by dividing the length of the dimension by the length of each cube:
8m ÷ 0.08m = 100 cubes in the 8m dimension
To find the total length of the line, we need to add the lengths in each dimension:
25 cubes × 0.08m/cube = 2m
50 cubes × 0.08m/cube = 4m
100 cubes × 0.08m/cube = 8m
The total length of the line formed by the cubes is then:
2m + 4m + 8m = 14m
Therefore, if the cubes were lined up, the line would be 14 meters long.
the length of each cube is the cube root of 8 cm^3
not 8 cm
Apologies for the confusion. You are correct. The length of each cube is the cube root of 8 cm³, which is equal to 2 cm.
To find the length of the line formed by the cubes, we need to calculate the number of cubes that can be arranged in each dimension and multiply by the length of each dimension.
The length of the line formed by the cubes in the 2m dimension can be found by dividing the length of the dimension by the length of each cube:
2m ÷ 0.02m = 100 cubes in the 2m dimension
The length of the line formed by the cubes in the 4m dimension can be found by dividing the length of the dimension by the length of each cube:
4m ÷ 0.02m = 200 cubes in the 4m dimension
The length of the line formed by the cubes in the 8m dimension can be found by dividing the length of the dimension by the length of each cube:
8m ÷ 0.02m = 400 cubes in the 8m dimension
To find the total length of the line, we need to add the lengths in each dimension:
100 cubes × 0.02m/cube = 2m
200 cubes × 0.02m/cube = 4m
400 cubes × 0.02m/cube = 8m
The total length of the line formed by the cubes is then:
2m + 4m + 8m = 14m
Therefore, if the cubes were lined up, the line would be 14 meters long.