A beam 9 m long, 40 cm wide and 20 cm high is made up of iron which weight 50kg per cubic metre. The weight of the beam is

Options

A. 27 kg
B. 48 kg
C. 36 kg
D. 56 kg

Answer

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

### Step 1: Convert the dimensions of the beam from centimeters to meters.
- Length (l) = 9 m (already in meters)
- Width (b) = 40 cm = 40/100 m = 0.4 m
- Height (h) = 20 cm = 20/100 m = 0.2 m

### Step 2: Calculate the volume of the beam.
The formula for the volume (V) of a rectangular prism (beam) is given by:
\[ V = l \times b \times h \]

Substituting the values:
\[ V = 9 \, \text{m} \times 0.4 \, \text{m} \times 0.2 \, \text{m} \]

Calculating the volume:
\[ V = 9 \times 0.4 \times 0.2 = 0.72 \, \text{m}^3 \]

### Step 3: Calculate the weight of the beam.
The weight of the beam can be calculated using the formula:
\[ \text{Weight} = \text{Volume} \times \text{Density} \]

Given that the density of iron is 50 kg/m³:
\[ \text{Weight} = 0.72 \, \text{m}^3 \times 50 \, \text{kg/m}^3 \]

Calculating the weight:
\[ \text{Weight} = 36 \, \text{kg} \]

### Final Answer:
The weight of the beam is **36 kg**.

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