How many cubes of side 5 cm can be made from a solid cube of side 10 cm ?

Answer

To solve the problem of how many cubes of side 5 cm can be made from a solid cube of side 10 cm, we will follow these steps:

### Step 1: Calculate the volume of the larger cube
The formula for the volume \( V \) of a cube with side length \( L \) is given by:
\[ V = L^3 \]
For the larger cube with a side of 10 cm:
\[ V_{\text{large}} = 10^3 = 10 \times 10 \times 10 = 1000 \text{ cm}^3 \]

### Step 2: Calculate the volume of the smaller cube
Using the same formula for the smaller cube with a side of 5 cm:
\[ V_{\text{small}} = 5^3 = 5 \times 5 \times 5 = 125 \text{ cm}^3 \]

### Step 3: Determine the number of smaller cubes that can fit into the larger cube
Let \( N \) be the number of smaller cubes that can fit into the larger cube. The total volume of the smaller cubes must equal the volume of the larger cube:
\[ N \times V_{\text{small}} = V_{\text{large}} \]
Substituting the volumes we calculated:
\[ N \times 125 = 1000 \]

### Step 4: Solve for \( N \)
To find \( N \), divide both sides by the volume of the smaller cube:
\[ N = \frac{1000}{125} \]
Calculating this gives:
\[ N = 8 \]

### Conclusion
Thus, the number of cubes of side 5 cm that can be made from a solid cube of side 10 cm is \( \boxed{8} \).

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