A matchbox measures 4 cm × 2.5 cm × 1.5 cm, what will be the volume of a packet containing 12 such boxes ?

Question

Accepted Answer

To determine the volume of a packet containing 12 matchboxes, we first need to calculate the volume of a single matchbox and then multiply it by the number of matchboxes in the packet.

1. **Volume of a Single Matchbox:**
   - The dimensions of a matchbox are given as 4 cm × 2.5 cm × 1.5 cm.
   - The volume of a rectangular box (or cuboid) is calculated using the formula:
     $$
     \text{Volume} = \text{length} \times \text{width} \times \text{height}
     $$
   - Substituting the given dimensions:
     $$
     \text{Volume of one matchbox} = 4 \, \text{cm} \times 2.5 \, \text{cm} \times 1.5 \, \text{cm} = 15 \, \text{cm}^3
     $$

2. **Volume of 12 Matchboxes:**
   - To find the total volume of 12 matchboxes, multiply the volume of one matchbox by 12:
     $$
     \text{Total Volume} = 15 \, \text{cm}^3 \times 12 = 180 \, \text{cm}^3
     $$

Therefore, the volume of a packet containing 12 such matchboxes is 180 cm³, which corresponds to Option 1.

**Explanation for Incorrect Options:**

- **Option 2 (140 cm³):** This option is incorrect because it does not match the calculated total volume of 180 cm³. The calculation clearly shows that multiplying the volume of one matchbox (15 cm³) by 12 results in 180 cm³, not 140 cm³.

- **Option 3 (120 cm³):** This option is incorrect for the same reason. The total volume of 12 matchboxes is 180 cm³, not 120 cm³. The calculation of 15 cm³ per matchbox multiplied by 12 confirms this.

- **Option 4 (100 cm³):** This option is also incorrect. The calculated total volume is 180 cm³, which is significantly different from 100 cm³. The multiplication of 15 cm³ by 12 clearly results in 180 cm³.

In conclusion, the correct answer is Option 1 (180 cm³), as it accurately reflects the total volume of a packet containing 12 matchboxes based on the given dimensions.