A right circular cylindrical tunnel of diameter 5 m and length 10 m is to be constructed from a sheet of iron. The area of iron sheet required will be :

Options

A. `52 pi`
B. `50 pi`
C. `51 pi`
D. `49 pi`

Answer

To find the area of the iron sheet required to construct a right circular cylindrical tunnel, we need to calculate the cylindrical surface area of the tunnel. The formula for the curved surface area (CSA) of a cylinder is given by:

\[ \text{CSA} = 2\pi rh \]

Where:
- \( r \) is the radius of the cylinder
- \( h \) is the height (or length) of the cylinder

### Step 1: Determine the radius
The diameter of the tunnel is given as 5 m. To find the radius, we use the formula:

\[ r = \frac{\text{diameter}}{2} \]

Substituting the value:

\[ r = \frac{5 \, \text{m}}{2} = 2.5 \, \text{m} \]

### Step 2: Identify the height (length) of the cylinder
The length of the tunnel is given as 10 m. Thus, we have:

\[ h = 10 \, \text{m} \]

### Step 3: Substitute the values into the formula
Now we can substitute the values of \( r \) and \( h \) into the formula for the curved surface area:

\[ \text{CSA} = 2\pi rh \]

Substituting \( r = 2.5 \, \text{m} \) and \( h = 10 \, \text{m} \):

\[ \text{CSA} = 2\pi (2.5 \, \text{m})(10 \, \text{m}) \]

### Step 4: Calculate the area
Now we calculate the area:

\[ \text{CSA} = 2\pi (25) \]

\[ \text{CSA} = 50\pi \]

### Step 5: Approximate the value
Using \( \pi \approx 3.14 \):

\[ \text{CSA} \approx 50 \times 3.14 = 157 \, \text{m}^2 \]

### Conclusion
The area of the iron sheet required to construct the tunnel is approximately \( 157 \, \text{m}^2 \).