How many planks of size 2 m × 35 cm × 8 cm can be made from a wooden block 8 m long, 70 cm wide and 40 cm thick ?

Question

Accepted Answer

To determine how many planks of size 2 m × 35 cm × 8 cm can be made from a wooden block measuring 8 m long, 70 cm wide, and 40 cm thick, we need to calculate the volume of both the wooden block and a single plank, and then see how many such planks can fit into the block.

1. **Convert all dimensions to the same unit:**

- The dimensions of the wooden block are 8 m × 70 cm × 40 cm. Converting meters to centimeters, we have:
     - Length: 8 m = 800 cm
     - Width: 70 cm
     - Thickness: 40 cm

- The dimensions of a plank are 2 m × 35 cm × 8 cm. Converting meters to centimeters, we have:
     - Length: 2 m = 200 cm
     - Width: 35 cm
     - Thickness: 8 cm

2. **Calculate the volume of the wooden block:**

$$
   \text{Volume of wooden block} = 800 \, \text{cm} \times 70 \, \text{cm} \times 40 \, \text{cm} = 2,240,000 \, \text{cm}^3
   $$

3. **Calculate the volume of a single plank:**

$$
   \text{Volume of a plank} = 200 \, \text{cm} \times 35 \, \text{cm} \times 8 \, \text{cm} = 56,000 \, \text{cm}^3
   $$

4. **Determine how many planks can be made:**

$$
   \text{Number of planks} = \frac{\text{Volume of wooden block}}{\text{Volume of a plank}} = \frac{2,240,000 \, \text{cm}^3}{56,000 \, \text{cm}^3} = 40
   $$

Thus, 40 planks can be made from the wooden block, which corresponds to Option 2.

**Explanation for why other options are incorrect:**

- **Option 1 (45):** This option suggests that more planks can be made than the calculated 40. However, based on the volume calculations, only 40 planks can fit within the given dimensions of the wooden block.

- **Option 3 (50):** This option suggests an even greater number of planks than Option 1. Given the volume constraints, it is not possible to produce 50 planks from the wooden block.

- **Option 4 (48):** Similar to the previous options, this number exceeds the calculated capacity of 40 planks. The volume of the wooden block does not support the production of 48 planks.

In conclusion, the calculations clearly show that Option 2 is the correct answer, as it accurately reflects the maximum number of planks that can be made from the given wooden block.