Answer: The volume of the metal cube 1x1x1 m is:
V_cube = l × w × h = 1 m × 1 m × 1 m = 1 m^3
The volume of the metal block that is to be cut from the cube is:
V_block = l × w × h = 3 cm × 3 cm × 4 cm = 36 cm^3
We need to convert the volume of the block to cubic meters, as the volume of the cube is given in cubic meters. We can use the conversion factor 1 m = 100 cm to convert cubic centimeters to cubic meters.
V_block = 36 cm^3 ÷ (100 cm/m)^3 = 0.000036 m^3
The number of blocks that can be cut from the cube is:
N_blocks = V_cube ÷ V_block = 1 m^3 ÷ 0.000036 m^3 = 27,777.78
Since we can only have a whole number of blocks, the maximum number of blocks that can be cut from the cube is 27,777.
The remaining volume of the cube after cutting the metal block is:
V_remain = V_cube - V_block × N_blocks = 1 m^3 - 0.000036 m^3 × 27,777 = 0.999 m^3
The surface area of the remaining cube can be calculated as follows:
S_remain = 6 × (l × w) = 6 × (h^2) = 6 × (0.999 m)^2 = 5.994 m^2
Therefore, the complete number of blocks that can be cut from the metal cube is 27,777. The volume of each block is 36 cm^3 or 0.000036 m^3. The remaining cube has a volume of 0.999 m^3 and a surface area of 5.994 m^2.
Explanation: