Respuesta :
Answer:
The number of cubes is which can the rectangular prism be cut into is 16.
Therefore total surface area of the all cubes is 384 cm².
The volume of all cubes is 128 cubic cm.
Step-by-step explanation:
Given that,
a rectangular prism is 8 cm long, 4 cm wide and 4 cm tall.
The dimensions of a cube is 2 cm × 2 cm × 2 cm.
Since the cubes cuts out from the rectangular prism.
So the volume of the rectangular prism= the volume of the cubes.
Let the number of cubes which cut out from the rectangular prism be x.
The volume of the rectangular prism is = (8×4×4) cubic cm
The volume of x cubes is =x (2×2×2)cubic cm
According to the problem,
x (2×2×2)=8×4×4
[tex]\Rightarrow x=\frac{8\times 4\times 4}{2\times2\times2}[/tex]
[tex]\Rightarrow x=16[/tex]
The number of cubes is which can the rectangular prism be cut into is 16.
The surface area of a cube is = 6× side²
Each sides of the cube are 2 cm.
The surface area of 16 cubes is =( 16×6×2²) cm²
=384 cm²
Therefore total surface area of the all cubes is 384 cm².
Since the volume of the rectangular prism= the volume of the cubes.
The volume of the rectangular prism is = (8×4×4) cubic cm
=128 cubic cm
The volume of all cubes is 128 cubic cm.
