Respuesta :
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,
[tex]V_1=l\times b\times h[/tex]
[tex]V_1=7\times 4\times 4[/tex]
[tex]V_1=112[/tex]
Therefore, the volume of rectangular prism is 112 cm square.
The volume of cubes is,
[tex]V_2=a^3[/tex]
[tex]V_2=(2)^3[/tex]
[tex]V_2=8[/tex]
The number of cubes in the rectangular prism is,
[tex]N=\frac{V_1}{V_2} =\frac{112}{8} =14[/tex]
Therefore, the number of cubes is 14.
Total surface area of a cube is,
[tex]A=6a^2[/tex]
[tex]A=6(2)^2[/tex]
[tex]A=24[/tex]
Total surface area of all cubes is,
[tex]14\times A=14\times 24=336[/tex]
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.
