How many 3 cm cubes can be cut from a cuboid measuring ` 18 xx 12 cm xx 9 cm ` ?

Answer

To find out how many 3 cm cubes can be cut from a cuboid measuring 18 cm x 12 cm x 9 cm, we can follow these steps:

### Step 1: Calculate the Volume of the Cuboid
The volume \( V \) of a cuboid can be calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
For our cuboid, the dimensions are:
- Length = 18 cm
- Width = 12 cm
- Height = 9 cm

So, the volume of the cuboid is:
\[ V = 18 \, \text{cm} \times 12 \, \text{cm} \times 9 \, \text{cm} \]
Calculating this gives:
\[ V = 1944 \, \text{cm}^3 \]

### Step 2: Calculate the Volume of One Cube
The volume \( V_c \) of a cube can be calculated using the formula:
\[ V_c = \text{side}^3 \]
For our cube, the side length is 3 cm. So, the volume of one cube is:
\[ V_c = 3 \, \text{cm} \times 3 \, \text{cm} \times 3 \, \text{cm} = 27 \, \text{cm}^3 \]

### Step 3: Calculate the Number of Cubes
To find the number of cubes \( n \) that can be cut from the cuboid, we divide the volume of the cuboid by the volume of one cube:
\[ n = \frac{\text{Volume of Cuboid}}{\text{Volume of One Cube}} = \frac{1944 \, \text{cm}^3}{27 \, \text{cm}^3} \]
Calculating this gives:
\[ n = 72 \]

### Final Answer
Thus, the number of 3 cm cubes that can be cut from the cuboid is:
\[ \boxed{72} \]

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