How many planks of size `2mxx25cmxx8cm` can be prepared from a wooden block 5 m long, 70 cm broad and 32 cm thick, assuming that there is no wastage?

Answer

To solve the problem of how many planks of size \(2m \times 25cm \times 8cm\) can be prepared from a wooden block measuring \(5m \times 70cm \times 32cm\), we will follow these steps:

### Step 1: Convert all measurements to the same unit
We will convert the dimensions of the planks and the wooden block into centimeters for consistency.

- **Plank dimensions:**
- Length: \(2m = 2 \times 100 = 200cm\)
- Breadth: \(25cm\)
- Thickness: \(8cm\)

- **Wooden block dimensions:**
- Length: \(5m = 5 \times 100 = 500cm\)
- Breadth: \(70cm\)
- Thickness: \(32cm\)

### Step 2: Calculate the volume of one plank
The volume \(V\) of a plank can be calculated using the formula:
\[ V = \text{Length} \times \text{Breadth} \times \text{Thickness} \]
Substituting the dimensions of the plank:
\[ V = 200cm \times 25cm \times 8cm \]
Calculating this gives:
\[ V = 200 \times 25 \times 8 = 40000 \, cm^3 \]

### Step 3: Calculate the volume of the wooden block
Using the same formula for volume, we calculate the volume of the wooden block:
\[ V = \text{Length} \times \text{Breadth} \times \text{Thickness} \]
Substituting the dimensions of the block:
\[ V = 500cm \times 70cm \times 32cm \]
Calculating this gives:
\[ V = 500 \times 70 \times 32 = 1120000 \, cm^3 \]

### Step 4: Determine the number of planks that can be made
To find the number of planks that can be prepared from the wooden block, we divide the volume of the block by the volume of one plank:
\[ \text{Number of planks} = \frac{\text{Volume of block}}{\text{Volume of plank}} = \frac{1120000 \, cm^3}{40000 \, cm^3} \]
Calculating this gives:
\[ \text{Number of planks} = \frac{1120000}{40000} = 28 \]

### Final Answer
Thus, the number of planks that can be prepared is **28**.

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