The number of planks of dimension (`4mxx50cmxx20cm`) that can be stored in a pit which is 16m long, 12m wide and 4m deep is.

Options

A. 1900
B. 1920
C. 1800
D. 1840

Answer

To solve the problem of how many planks can be stored in a pit, we need to follow these steps:

### Step 1: Convert all dimensions to the same unit
The dimensions of the planks are given as:
- Length (L) = 4 m
- Breadth (B) = 50 cm
- Height (H) = 20 cm

We will convert the length of the planks from meters to centimeters:
- \( L = 4 \, \text{m} = 4 \times 100 = 400 \, \text{cm} \)

Now, the dimensions of the planks in centimeters are:
- Length = 400 cm
- Breadth = 50 cm
- Height = 20 cm

### Step 2: Calculate the volume of one plank
The volume (V) of one plank can be calculated using the formula:
\[ V = L \times B \times H \]
Substituting the values:
\[ V = 400 \, \text{cm} \times 50 \, \text{cm} \times 20 \, \text{cm} \]
\[ V = 400 \times 50 \times 20 = 400000 \, \text{cm}^3 \]

### Step 3: Determine the dimensions of the pit
The dimensions of the pit are given as:
- Length = 16 m
- Width = 12 m
- Depth = 4 m

We will convert these dimensions to centimeters:
- Length = \( 16 \, \text{m} = 16 \times 100 = 1600 \, \text{cm} \)
- Width = \( 12 \, \text{m} = 12 \times 100 = 1200 \, \text{cm} \)
- Depth = \( 4 \, \text{m} = 4 \times 100 = 400 \, \text{cm} \)

### Step 4: Calculate the volume of the pit
The volume of the pit can be calculated using the formula:
\[ V_{\text{pit}} = \text{Length} \times \text{Width} \times \text{Depth} \]
Substituting the values:
\[ V_{\text{pit}} = 1600 \, \text{cm} \times 1200 \, \text{cm} \times 400 \, \text{cm} \]
\[ V_{\text{pit}} = 1600 \times 1200 \times 400 = 768000000 \, \text{cm}^3 \]

### Step 5: Calculate the number of planks that can fit in the pit
Let \( n \) be the number of planks that can fit in the pit. The total volume of the planks must equal the volume of the pit:
\[ n \times V_{\text{plank}} = V_{\text{pit}} \]
Substituting the volumes:
\[ n \times 400000 \, \text{cm}^3 = 768000000 \, \text{cm}^3 \]
To find \( n \):
\[ n = \frac{768000000}{400000} \]
\[ n = 1920 \]

### Final Answer
The number of planks that can be stored in the pit is **1920**.

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