How many cubes having edge of 4 inches each can be cut from a cube having edge of 12 inches ?

Answer

To solve the problem of how many smaller cubes with an edge of 4 inches each can be cut from a larger cube with an edge of 12 inches, we can follow these steps:

### Step 1: Calculate the volume of the larger cube.
The formula for the volume \( V \) of a cube is given by:
\[ V = \text{edge}^3 \]
For the larger cube with an edge of 12 inches:
\[ V_{\text{large}} = 12^3 = 12 \times 12 \times 12 = 1728 \text{ cubic inches} \]

### Step 2: Calculate the volume of the smaller cube.
Using the same formula for the smaller cube with an edge of 4 inches:
\[ V_{\text{small}} = 4^3 = 4 \times 4 \times 4 = 64 \text{ cubic inches} \]

### Step 3: Determine how many smaller cubes can fit into the larger cube.
To find the number of smaller cubes that can be cut from the larger cube, we divide the volume of the larger cube by the volume of the smaller cube:
\[ \text{Number of smaller cubes} = \frac{V_{\text{large}}}{V_{\text{small}}} = \frac{1728}{64} \]

### Step 4: Perform the division.
Calculating the division:
\[ \frac{1728}{64} = 27 \]

### Conclusion:
Thus, the number of smaller cubes with an edge of 4 inches that can be cut from the larger cube with an edge of 12 inches is **27**.

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