Find the dimension of a box that will hold half as many cubes as a box that is 2 by 8 by 10.
To find the dimension of a box that will hold half as many cubes as a box that is 2 by 8 by 10, we need to determine the volume of the larger box and then divide it by 2.
The volume of a rectangular box is calculated by multiplying its length, width, and height.
Volume of the larger box = length * width * height
= 2 * 8 * 10
= 160 cubic units
Since we want to find a box that will hold half as many cubes, we need the volume of the smaller box to be equal to 160/2 = 80 cubic units.
Let's assume the dimensions of the smaller box are x, y, and z.
The volume of the smaller box is then given by:
x * y * z = 80 cubic units
To find the dimensions, we need to determine three positive integers (x, y, z) that multiply to give 80. We will start by listing all possible factors of 80.
Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Now, we can try different combinations of these factors to find the ones whose product equals 80. Let's list a few possibilities:
1 * 1 * 80 = 80
1 * 2 * 40 = 80
2 * 2 * 20 = 80
4 * 4 * 5 = 80
...
From these combinations, we can see that 4, 4, and 5 is a valid set of dimensions for the smaller box. Thus, a box with dimensions 4 by 4 by 5 can hold half as many cubes as a box that is 2 by 8 by 10.
To find the dimensions of a box that can hold half as many cubes as a given box, we need to consider the volume of the given box and then determine the dimensions of the other box that have half that volume.
The volume of a box is calculated by multiplying its length, width, and height.
Given that the box has dimensions of 2 by 8 by 10, the volume can be calculated as follows:
Volume = length * width * height
Volume = 2 * 8 * 10 = 160 cubic units
To find the dimensions of a box that holds half as many cubes, we need to find a new volume that is half of 160 cubic units.
Half of 160 cubic units is 80 cubic units.
To determine the dimensions, we need to find two numbers whose product is 80, with one factor being as close as possible to the square root of 80.
The square root of 80 is approximately 8.94.
Factors of 80 include: 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.
Since one dimension should be as close as possible to 8.94, we can select 8 as the first dimension.
Dividing 80 by 8 gives us 10, which can be chosen as the second dimension.
Therefore, the dimensions of the box that can hold half as many cubes are 8 by 10.
It is important to note that there might be multiple solutions to this problem, but this explanation provides one valid approach.
2 * 8 * 10 = 160 cubes
What are the dimensions of a box that holds 80 cubes?