A certain type of cube has 2-inch edges. What is the maximum number of cubes than can be put into a box that measures 2.7 feet by 3.2 feet by 4.1 feet?
To find the maximum number of cubes that can fit inside the given box, we need to calculate the volume of the box and compare it to the volume of a single cube.
First, let's convert the dimensions of the box from feet to inches to ensure consistent units:
2.7 feet = 32.4 inches
3.2 feet = 38.4 inches
4.1 feet = 49.2 inches
Now, let's calculate the volume of the box:
Volume of the box = length * width * height
Volume of the box = 32.4 inches * 38.4 inches * 49.2 inches
Volume of the box = 197,297.28 cubic inches
Next, let's calculate the volume of a single cube:
Volume of a cube = edge length * edge length * edge length
Volume of a cube = 2 inches * 2 inches * 2 inches
Volume of a cube = 8 cubic inches
Now, we can determine the maximum number of cubes that can fit inside the box by dividing the volume of the box by the volume of a single cube:
Maximum number of cubes = Volume of the box / Volume of a cube
Maximum number of cubes = 197,297.28 cubic inches / 8 cubic inches
Maximum number of cubes ≈ 24,662.16
Since the number of cubes must be a whole number, we need to round down to the nearest whole number:
Maximum number of cubes = 24,662
Therefore, the maximum number of cubes that can fit into the given box is 24,662.