Question

If you have a cube measuring 1 unit on each side, how many of those cubes would fit into a space 2 units by 3 units by 4 units

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Answer 1

Given:

Measure of a cube = 1 unit on each side.

Dimensions of a space 2 units by 3 units by 4 units.

To find:

Number of cubes that can be fit into the given space.

Solution:

The volume of cube is:

`V_1=a^3`

Where, a is the side length of cube.

`V_1=(1)^3`

`V_1=1`

So, the volume of the cube is 1 cubic units.

The volume of the cuboid is:

`V_2=l* b* h`

Where, l is length, w is width and h is height.

Putting
`l=2,b=3,h=4`, we get

`V_2=2* 3* 4`

`V_2=24`

So, the volume of the space is 24 cubic units.

We need to divide the volume of the space by the volume of the cube to find the number of cubes that can be fit into the given space.

`n=(V_2)/(V_1)`

`n=(24)/(1)`

`n=24`

Therefore, 24 cubes can be fit into the given space.