Question

Answer the following questions about a cube that is 4 cm on a side made of four differentcolored-red, blue, green, and yellow-layers, from top to bottom respectively, of smaller cubes that are 1 cm on a side.1) How many cubes of each color are in the large cube? How do you know?

Answer 1

The number of smaller cubes of each color in the large cube is;

`16`

Step-by-step explanation:

Given that the larger cube is 4 cm on the side.

The Volume of the larger cube is;

`\begin{gathered} V=l^3=4^3 \\ V=64cm^3 \end{gathered}`

For the smaller cubes with side length 1 cm, its volume is;

`v=1^{3^{}}=1cm^3`

The total number of smaller cubes will be; is the volume of the larger cube divided by the volume of the smaller cube.

`\begin{gathered} N=(V)/(v)=(64)/(1) \\ N=64 \end{gathered}`

For each color, the number of cubes of each color will be;

`\begin{gathered} n=(N)/(4)=(64)/(4) \\ n=16 \end{gathered}`

Therefore, the number of smaller cubes of each color in the large cube is;

`16`