An iron beam is 4 m long, 40 cm broad and 30 cm thick. Its weight in Kilogram, if 1 cu cm of iron weight 8 gm is

Options

A. 384
B. 3840
C. 38400
D. 38.4

Answer

To find the weight of the iron beam, we will follow these steps:

### Step 1: Convert all dimensions to the same unit
The dimensions of the beam are given as:
- Length = 4 m
- Width = 40 cm
- Thickness = 30 cm

First, we need to convert the length from meters to centimeters:
1 m = 100 cm
So, 4 m = 4 × 100 = 400 cm

Now, we have:
- Length = 400 cm
- Width = 40 cm
- Thickness = 30 cm

### Step 2: Calculate the volume of the beam
The volume \( V \) of a rectangular prism (the iron beam) is calculated using the formula:
\[ V = \text{Length} \times \text{Width} \times \text{Thickness} \]

Substituting the values:
\[ V = 400 \, \text{cm} \times 40 \, \text{cm} \times 30 \, \text{cm} \]

Calculating the volume:
\[ V = 400 \times 40 = 16000 \, \text{cm}^2 \]
\[ V = 16000 \times 30 = 480000 \, \text{cm}^3 \]

### Step 3: Calculate the weight of the beam
We know that 1 cubic centimeter of iron weighs 8 grams. Therefore, the weight \( W \) of the beam can be calculated as:
\[ W = V \times \text{Weight per cubic cm} \]
\[ W = 480000 \, \text{cm}^3 \times 8 \, \text{g/cm}^3 \]

Calculating the weight:
\[ W = 480000 \times 8 = 3840000 \, \text{grams} \]

### Step 4: Convert grams to kilograms
To convert grams to kilograms, we divide by 1000:
\[ W = \frac{3840000 \, \text{grams}}{1000} = 3840 \, \text{kg} \]

### Final Answer
The weight of the iron beam is **3840 kg**.

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