To solve the problem of how many soap cakes can be packed into two boxes, we will follow these steps:
### Step 1: Calculate the volume of one soap cake.
The dimensions of the soap cake are given as:
- Length = 7 cm
- Breadth = 5 cm
- Height = 2.5 cm
The volume \( V \) of a cuboid is calculated using the formula:
\[
V = \text{Length} \times \text{Breadth} \times \text{Height}
\]
Substituting the values:
\[
V = 7 \, \text{cm} \times 5 \, \text{cm} \times 2.5 \, \text{cm}
\]
Calculating this:
\[
V = 7 \times 5 = 35 \, \text{cm}^2
\]
\[
V = 35 \times 2.5 = 87.5 \, \text{cm}^3
\]
### Step 2: Calculate the volume of one box.
The dimensions of each box are given as:
- Length = 56 cm
- Breadth = 0.4 m (which we need to convert to cm)
- Height = 0.25 m (which we also need to convert to cm)
Converting the dimensions from meters to centimeters:
- \( 0.4 \, \text{m} = 0.4 \times 100 = 40 \, \text{cm} \)
- \( 0.25 \, \text{m} = 0.25 \times 100 = 25 \, \text{cm} \)
Now, we can calculate the volume of one box:
\[
V_{\text{box}} = \text{Length} \times \text{Breadth} \times \text{Height}
\]
Substituting the values:
\[
V_{\text{box}} = 56 \, \text{cm} \times 40 \, \text{cm} \times 25 \, \text{cm}
\]
Calculating this:
\[
V_{\text{box}} = 56 \times 40 = 2240 \, \text{cm}^2
\]
\[
V_{\text{box}} = 2240 \times 25 = 56000 \, \text{cm}^3
\]
### Step 3: Calculate the volume of two boxes.
Since we have two boxes, the total volume will be:
\[
V_{\text{total}} = 2 \times V_{\text{box}} = 2 \times 56000 \, \text{cm}^3 = 112000 \, \text{cm}^3
\]
### Step 4: Calculate the maximum number of soap cakes that can fit into the two boxes.
To find the maximum number of soap cakes that can fit, we divide the total volume of the boxes by the volume of one soap cake:
\[
\text{Number of soap cakes} = \frac{V_{\text{total}}}{V_{\text{soap}}} = \frac{112000 \, \text{cm}^3}{87.5 \, \text{cm}^3}
\]
Calculating this:
\[
\text{Number of soap cakes} = \frac{112000}{87.5} = 1280
\]
Thus, the maximum number of soap cakes that can be packed into the two boxes is **1280**.
