To solve the problem step by step, we will calculate the volumes of the cuboidal box and the cubical box, then determine how many 1 cm³ cubes can be packed into these boxes, and finally find out how many cubes will remain unpacked.
### Step 1: Calculate the volume of the cuboidal box.
The formula for the volume of a cuboid is:
\[
\text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height}
\]
Given dimensions:
- Length = 13 cm
- Breadth = 11 cm
- Height = 9 cm
Calculating the volume:
\[
\text{Volume of cuboidal box} = 13 \, \text{cm} \times 11 \, \text{cm} \times 9 \, \text{cm} = 1287 \, \text{cm}^3
\]
### Step 2: Calculate the volume of the cubical box.
The formula for the volume of a cube is:
\[
\text{Volume} = \text{Side}^3
\]
Given side:
- Side = 12 cm
Calculating the volume:
\[
\text{Volume of cubical box} = 12 \, \text{cm} \times 12 \, \text{cm} \times 12 \, \text{cm} = 1728 \, \text{cm}^3
\]
### Step 3: Calculate the total volume available for packing.
Now, we add the volumes of both boxes:
\[
\text{Total volume} = \text{Volume of cuboidal box} + \text{Volume of cubical box}
\]
Calculating the total volume:
\[
\text{Total volume} = 1287 \, \text{cm}^3 + 1728 \, \text{cm}^3 = 3015 \, \text{cm}^3
\]
### Step 4: Calculate the total volume of the small cubes.
Each small cube has a side of 1 cm, so its volume is:
\[
\text{Volume of small cube} = 1 \, \text{cm}^3
\]
Given that Tanu wants to pack 3060 small cubes, the total volume of these cubes is:
\[
\text{Total volume of small cubes} = 3060 \, \text{cubes} \times 1 \, \text{cm}^3 = 3060 \, \text{cm}^3
\]
### Step 5: Calculate how many cubes can be packed.
Now, we find out how many cubes can actually be packed in the total volume available:
\[
\text{Cubes packed} = \frac{\text{Total volume}}{\text{Volume of small cube}} = \frac{3015 \, \text{cm}^3}{1 \, \text{cm}^3} = 3015 \, \text{cubes}
\]
### Step 6: Calculate the number of unpacked cubes.
Finally, we find the number of unpacked cubes:
\[
\text{Unpacked cubes} = \text{Total cubes} - \text{Cubes packed} = 3060 - 3015 = 45
\]
### Final Answer:
The number of cubes left unpacked in these boxes is **45**.
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