A soap cake measures 7 cm in length, 5 cm in breadth and 2.5 cm in height. How many soapcakes can be placed in a cardboard box whose length, breadth and height are, respectively, 56 cm, 40 cm and 25 cm?

Options

A. 64
B. 640
C. 6400
D. 6440

Answer

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

### Step 1: Calculate the volume of one soap cake.
The formula for the volume \( V \) of a cuboid is given by:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
For the soap cake:
- Length = 7 cm
- Breadth = 5 cm
- Height = 2.5 cm

So, the volume of one soap cake is:
\[ V_{\text{soap cake}} = 7 \, \text{cm} \times 5 \, \text{cm} \times 2.5 \, \text{cm} \]
Calculating this:
\[ V_{\text{soap cake}} = 7 \times 5 \times 2.5 = 87.5 \, \text{cm}^3 \]

### Step 2: Calculate the volume of the cardboard box.
Using the same volume formula for the box:
- Length = 56 cm
- Breadth = 40 cm
- Height = 25 cm

So, the volume of the cardboard box is:
\[ V_{\text{box}} = 56 \, \text{cm} \times 40 \, \text{cm} \times 25 \, \text{cm} \]
Calculating this:
\[ V_{\text{box}} = 56 \times 40 \times 25 = 56000 \, \text{cm}^3 \]

### Step 3: Determine how many soap cakes can fit in the box.
To find the number of soap cakes that can fit in the box, divide the volume of the box by the volume of one soap cake:
\[ \text{Number of soap cakes} = \frac{V_{\text{box}}}{V_{\text{soap cake}}} \]
Substituting the values:
\[ \text{Number of soap cakes} = \frac{56000 \, \text{cm}^3}{87.5 \, \text{cm}^3} \]
Calculating this:
\[ \text{Number of soap cakes} = 640 \]

### Final Answer:
Thus, the number of soap cakes that can be placed in the cardboard box is **640**.

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