- #1
Werg22
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You have a 3x3x3 cube, built with 1x1x1 bricks (27 bricks in total). You remove two diagonally opposite bricks (long diagonals). Can you build the remaining figure from 2xx1x1 bricks?
The volume of the cube can be calculated by multiplying the length, width, and height. In this case, the length, width, and height are all 3, so the volume is 3 x 3 x 3 = 27 cubic units.
The cube has 6 faces, with each face being a square.
The surface area of the cube can be calculated by finding the area of each face and then adding them together. In this case, the area of each face is 3 x 3 = 9 square units, so the total surface area is 6 x 9 = 54 square units.
Since the cube is made of 27 bricks, each with a unique position, there are a total of 27! (27 factorial) ways the cube can be assembled. This is equivalent to approximately 10.2 trillion possible combinations.
The mass of the cube will vary depending on the material the bricks are made of. Assuming each brick weighs 1 unit, the total mass of the cube would be 27 units.