Answer: The number of 2 times 2 times 2 cm cubes is 14. The total surface area of all the 2 times 2 times 2 times cm cubes is 336 cm square. The total volume of all the 2 times 2 times 2 times cm cubes is 112 cm cube.
Explanation:
It is given that the A rectangular prism is 7 cm long, 4 cm wide and 4 cm tall.
The volume of rectangular prism is,
![V_1=l\times b\times h](https://tex.z-dn.net/?f=V_1%3Dl%5Ctimes%20b%5Ctimes%20h)
![V_1=7\times 4\times 4](https://tex.z-dn.net/?f=V_1%3D7%5Ctimes%204%5Ctimes%204)
![V_1=112](https://tex.z-dn.net/?f=V_1%3D112)
Therefore, the volume of rectangular prism is 112 cm square.
The volume of cubes is,
![V_2=a^3](https://tex.z-dn.net/?f=V_2%3Da%5E3)
![V_2=(2)^3](https://tex.z-dn.net/?f=V_2%3D%282%29%5E3)
![V_2=8](https://tex.z-dn.net/?f=V_2%3D8)
The number of cubes in the rectangular prism is,
![N=\frac{V_1}{V_2} =\frac{112}{8} =14](https://tex.z-dn.net/?f=N%3D%5Cfrac%7BV_1%7D%7BV_2%7D%20%3D%5Cfrac%7B112%7D%7B8%7D%20%3D14)
Therefore, the number of cubes is 14.
Total surface area of a cube is,
![A=6a^2](https://tex.z-dn.net/?f=A%3D6a%5E2)
![A=6(2)^2](https://tex.z-dn.net/?f=A%3D6%282%29%5E2)
![A=24](https://tex.z-dn.net/?f=A%3D24)
Total surface area of all cubes is,
![14\times A=14\times 24=336](https://tex.z-dn.net/?f=14%5Ctimes%20A%3D14%5Ctimes%2024%3D336)
Therefore the total surface area of all cubes is 336 cm square.
Total volume of all cubes is equal t the volume of rectangular prism, i.e, 112 cm cube.