If the students were given 80cm square of wooden board to make a box, what is the largest cube they can make with the board?
80/6=15 = face on one side
so, the side of the cube is √15.
To determine the largest cube that can be made with the given wooden board, we first need to calculate the surface area of the board.
Given that the wooden board is a square with a side length of 80 cm, the formula to find the surface area of a square is:
Surface area = side length * side length
Substituting the value, we have:
Surface area = 80 cm * 80 cm = 6400 cm²
Now, let's consider a cube. A cube has 6 identical square faces, so the total surface area of a cube is given by:
Total surface area of cube = 6 * surface area of one face
In this case, the total surface area of the cube should not exceed the surface area of the wooden board. Therefore, we can equate the two:
6 * surface area of one face = 6400 cm²
Next, let's determine the surface area of one face of the cube:
Surface area of one face = (Side length of cube)²
Substituting this into the equation above, we get:
6 * (Side length of cube)² = 6400 cm²
Dividing both sides by 6, we have:
(Side length of cube)² = (6400 cm²) / 6
(Side length of cube)² = 1066.67 cm²
Now, take the square root of both sides to find the length of one side of the cube:
Side length of cube = √(1066.67 cm²)
Side length of cube ≈ 32.68 cm
Therefore, the largest cube that can be made with the given wooden board has a side length of approximately 32.68 cm.