Find the maximum number of soaps of size ` 2 cm xx 3 cm xx 5 cm ` that can be kept in a cuboidal box of dimensions `6 cm xx 3 cm xx 15 cm`.

Answer

To find the maximum number of soaps of size \(2 \, \text{cm} \times 3 \, \text{cm} \times 5 \, \text{cm}\) that can fit into a cuboidal box of dimensions \(6 \, \text{cm} \times 3 \, \text{cm} \times 15 \, \text{cm}\), we will follow these steps:

### Step 1: Identify the dimensions of the soap and the box
- Dimensions of the soap: \(2 \, \text{cm} \times 3 \, \text{cm} \times 5 \, \text{cm}\)
- Dimensions of the box: \(6 \, \text{cm} \times 3 \, \text{cm} \times 15 \, \text{cm}\)

### Step 2: Calculate how many soaps can fit along each dimension of the box
1. **Along the length (6 cm)**:
\[ \text{Number of soaps along length} = \frac{\text{Length of box}}{\text{Length of soap}} = \frac{6 \, \text{cm}}{2 \, \text{cm}} = 3 \]

2. **Along the width (3 cm)**:
\[ \text{Number of soaps along width} = \frac{\text{Width of box}}{\text{Width of soap}} = \frac{3 \, \text{cm}}{3 \, \text{cm}} = 1 \]

3. **Along the height (15 cm)**:
\[ \text{Number of soaps along height} = \frac{\text{Height of box}}{\text{Height of soap}} = \frac{15 \, \text{cm}}{5 \, \text{cm}} = 3 \]

### Step 3: Calculate the total number of soaps that can fit in the box
To find the total number of soaps that can fit in the box, we multiply the number of soaps that fit along each dimension:
\[ \text{Total number of soaps} = (\text{Number along length}) \times (\text{Number along width}) \times (\text{Number along height}) = 3 \times 1 \times 3 = 9 \]

### Final Answer
The maximum number of soaps that can be kept in the cuboidal box is **9**.

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