How many cubes, each of edge 3 cm, can be from a cube of edge 15 cm ?

Options

A. 25
B. 27
C. 125
D. 144

Answer

To find out how many smaller cubes of edge 3 cm can be formed from a larger cube of edge 15 cm, 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 15 cm:
\[ V_{\text{large}} = 15^3 = 15 \times 15 \times 15 \]
Calculating this:
\[ 15 \times 15 = 225 \]
\[ 225 \times 15 = 3375 \text{ cm}^3 \]
So, the volume of the larger cube is \( 3375 \text{ cm}^3 \).

### Step 2: Calculate the volume of the smaller cube.
Now, we calculate the volume of the smaller cube with an edge of 3 cm:
\[ V_{\text{small}} = 3^3 = 3 \times 3 \times 3 \]
Calculating this:
\[ 3 \times 3 = 9 \]
\[ 9 \times 3 = 27 \text{ cm}^3 \]
So, the volume of the smaller cube is \( 27 \text{ cm}^3 \).

### Step 3: Determine how many smaller cubes can fit into the larger cube.
To find the number of smaller cubes that can fit into the larger cube, we divide the volume of the larger cube by the volume of the smaller cube:
\[ \text{Number of smaller cubes} = \frac{V_{\text{large}}}{V_{\text{small}}} = \frac{3375}{27} \]
Calculating this:
\[ \frac{3375}{27} = 125 \]
Thus, the number of smaller cubes that can be formed from the larger cube is \( 125 \).

### Final Answer:
The answer is \( 125 \).

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