A soap cake is of sie `8 cm xx 5 cm xx 4 cm`. The numberof such soap cakes that can be packed in a box measuring `56 xx 35 cm xx 28 cm` is :

Options

A. 49
B. 196
C. 243
D. 343

Answer

To find the number of soap cakes that can be packed in a box, we need to follow these steps:

### Step 1: Calculate the volume of the soap cake
The volume of a rectangular object can be calculated using the formula:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]

For the soap cake with dimensions \(8 \, \text{cm} \times 5 \, \text{cm} \times 4 \, \text{cm}\):
\[ \text{Volume of soap cake} = 8 \times 5 \times 4 \]
Calculating this:
\[ 8 \times 5 = 40 \]
\[ 40 \times 4 = 160 \, \text{cm}^3 \]
So, the volume of one soap cake is \(160 \, \text{cm}^3\).

### Step 2: Calculate the volume of the box
Using the same formula for the box with dimensions \(56 \, \text{cm} \times 35 \, \text{cm} \times 28 \, \text{cm}\):
\[ \text{Volume of box} = 56 \times 35 \times 28 \]
Calculating this step by step:
\[ 56 \times 35 = 1960 \]
\[ 1960 \times 28 = 54880 \, \text{cm}^3 \]
So, the volume of the box is \(54880 \, \text{cm}^3\).

### Step 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:
\[ \text{Number of soap cakes} = \frac{\text{Volume of box}}{\text{Volume of soap cake}} = \frac{54880}{160} \]
Calculating this:
\[ \frac{54880}{160} = 343 \]

### Conclusion
The number of soap cakes that can be packed in the box is \(343\).

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