A solid cube of edge 14 cm is melted down and recast into smaller and equal cubes each of edge 2 cm . Find the number of smaller cubes obtained.

Answer

To find the number of smaller cubes obtained from melting down a solid cube, we can follow these steps:

### Step 1: Calculate the volume of the larger cube.
The formula for the volume \( V \) of a cube with edge length \( a \) is given by:
\[ V = a^3 \]
For the larger cube with an edge length of 14 cm:
\[ V_{\text{large}} = 14^3 \]

### Step 2: Compute \( 14^3 \).
Calculating \( 14^3 \):
\[ 14^3 = 14 \times 14 \times 14 = 196 \times 14 = 2744 \text{ cm}^3 \]

### Step 3: Calculate the volume of one smaller cube.
Using the same formula for the smaller cubes, where the edge length is 2 cm:
\[ V_{\text{small}} = 2^3 \]

### Step 4: Compute \( 2^3 \).
Calculating \( 2^3 \):
\[ 2^3 = 2 \times 2 \times 2 = 8 \text{ cm}^3 \]

### Step 5: Set up the equation for the number of smaller cubes.
Let \( n \) be the number of smaller cubes. The total volume of the larger cube is equal to the total volume of the smaller cubes:
\[ V_{\text{large}} = n \times V_{\text{small}} \]
Substituting the volumes we calculated:
\[ 2744 = n \times 8 \]

### Step 6: Solve for \( n \).
To find \( n \), divide both sides by 8:
\[ n = \frac{2744}{8} \]

### Step 7: Compute \( \frac{2744}{8} \).
Calculating \( \frac{2744}{8} \):
\[ n = 343 \]

### Final Answer:
The number of smaller cubes obtained is \( 343 \).

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