How many cubes of edge 3 cm can be formed from a wooden piece of dimensions `36 cm xx 24 cm xx 18cm` ?

Answer

To solve the problem of how many cubes of edge 3 cm can be formed from a wooden piece with dimensions 36 cm x 24 cm x 18 cm, we will follow these steps:

### Step 1: Calculate the volume of the wooden piece.
The volume \( V \) of a rectangular prism (wooden piece) can be calculated using the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
Given dimensions:
- Length = 36 cm
- Breadth = 24 cm
- Height = 18 cm

Substituting the values:
\[ V = 36 \, \text{cm} \times 24 \, \text{cm} \times 18 \, \text{cm} \]

### Step 2: Perform the multiplication.
Calculating the volume:
\[ V = 36 \times 24 = 864 \, \text{cm}^2 \]
Now, multiply by the height:
\[ V = 864 \times 18 = 15552 \, \text{cm}^3 \]

### Step 3: Calculate the volume of one cube.
The volume \( V_c \) of a cube with edge length \( a \) is given by:
\[ V_c = a^3 \]
For a cube with edge length 3 cm:
\[ V_c = 3 \, \text{cm} \times 3 \, \text{cm} \times 3 \, \text{cm} = 27 \, \text{cm}^3 \]

### Step 4: Calculate the number of cubes that can be formed.
To find the number of cubes that can be formed from the wooden piece, divide the volume of the wooden piece by the volume of one cube:
\[ \text{Number of cubes} = \frac{V}{V_c} = \frac{15552 \, \text{cm}^3}{27 \, \text{cm}^3} \]

### Step 5: Perform the division.
Calculating the number of cubes:
\[ \text{Number of cubes} = \frac{15552}{27} = 576 \]

### Final Answer:
Thus, the number of cubes of edge 3 cm that can be formed from the wooden piece is **576**.

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