Number of cuboids with dimensions 8cm x 15cm x 20cm stacked together to form a h cube is
LCM(8,15,20) = 120
so you can form a cube of side 120 using 8*15*6 = 720 cuboids
To find the number of cuboids that can be stacked together to form a perfect cube, we need to calculate the volume of the cube and then divide it by the volume of one cuboid.
1. Calculate the volume of the cube:
Since all the dimensions of a cube are equal, we need to find the common dimension (h) of the cube. We can do this by taking the cube root of the volume of the cuboids. Using the formula for volume of a cuboid (length x width x height), we find that the volume of one cuboid is: 8 cm x 15 cm x 20 cm = 2400 cm^3.
2. Find the cube root of the volume of the cuboids:
We take the cube root of 2400 cm^3 to find the value of h, the dimension of the cube.
Cube root of 2400 cm^3 ≈ 13.42 (rounded to two decimal places)
Therefore, h ≈ 13.42 cm.
3. Calculate the volume of the cube:
The volume of the cube is given by h^3.
Volume of the cube = (13.42 cm)^3 = 2479.41 cm^3 (rounded to two decimal places).
4. Divide the volume of the cube by the volume of one cuboid:
Number of cuboids = Volume of the cube / Volume of one cuboid
Number of cuboids = 2479.41 cm^3 / 2400 cm^3 ≈ 1.03
Therefore, you can stack approximately 1 cuboid with dimensions 8 cm x 15 cm x 20 cm to form a perfect cube with dimensions approximately 13.42 cm x 13.42 cm x 13.42 cm.
To find the number of cuboids with dimensions 8cm x 15cm x 20cm that can be stacked together to form a larger cube, we need to calculate the volume of both the smaller cuboid and the larger cube.
The volume of the smaller cuboid is calculated by multiplying its length, width, and height:
Volume of smaller cuboid = 8cm x 15cm x 20cm = 2400 cm^3
The volume of a cube is calculated by raising one side length to the power of 3:
Volume of larger cube = h^3 (h = side length of the cube)
Since both the smaller cuboid and the larger cube have the same volume, we can set up the equation:
h^3 = 2400 cm^3
To find the value of h, we need to take the cube root of both sides of the equation:
h = ∛2400 cm^3
Using a calculator, we find that the cube root of 2400 is approximately 13.157.
Therefore, the side length of the larger cube, h, is approximately 13.157 cm.
Since the given dimensions of the smaller cuboid do not match the side length of the larger cube exactly, it is not possible to stack the smaller cuboids together to form a complete cube.