At the most , how many cakes of soap dimensions 8 cm `xx` 6 cm `xx` 4 cm can be placed in a wooden box of inner measures 28 cm `xx` 16 cm `xx`12 cm ?

Options

A. 35
B. 24
C. 28
D. 36

Answer

To find out how many cakes of soap can fit into the wooden box, we will calculate the volume of both the soap cakes and the wooden box, and then divide the volume of the box by the volume of one soap cake.

### Step-by-Step Solution:

1. **Calculate the Volume of the Wooden Box:**
- The dimensions of the wooden box are 28 cm x 16 cm x 12 cm.
- Volume of the box (V_box) = Length × Breadth × Height
- V_box = 28 cm × 16 cm × 12 cm
- V_box = 5376 cm³

2. **Calculate the Volume of One Cake of Soap:**
- The dimensions of the soap cake are 8 cm x 6 cm x 4 cm.
- Volume of one soap cake (V_soap) = Length × Breadth × Height
- V_soap = 8 cm × 6 cm × 4 cm
- V_soap = 192 cm³

3. **Calculate the Number of Soap Cakes that Can Fit in the Box:**
- To find the number of soap cakes that can fit in the box, we divide the volume of the box by the volume of one soap cake.
- Number of soap cakes = V_box / V_soap
- Number of soap cakes = 5376 cm³ / 192 cm³
- Number of soap cakes = 28

### Final Answer:
At most, **28 cakes of soap** can be placed in the wooden box.