If a right circular cylinder tunnel of diameter 2 m and length 40 m is to be instructed from a sheet of iron. Then, the area of iron sheet required (in `m^ 2`) is
(a) `40 pi`
(b) `60 pi`
(c) `80 pi`
(d) `100 pi`

Options

A. `40 pi`
B. `60 pi`
C. `80 pi`
D. `100 pi`

Answer

To find the area of the iron sheet required to construct a right circular cylinder tunnel, we need to calculate the lateral surface area of the cylinder. Since the tunnel is open at both ends, we will not include the area of the top and bottom circles.

### Step-by-Step Solution:

1. **Identify the given values:**
- Diameter of the cylinder (d) = 2 m
- Length of the cylinder (h) = 40 m

2. **Calculate the radius (r):**
- The radius is half of the diameter.
\[ r = \frac{d}{2} = \frac{2}{2} = 1 \text{ m} \]

3. **Use the formula for the lateral surface area of a cylinder:**
- The formula for the lateral surface area (A) of a cylinder is:
\[ A = 2 \pi r h \]

4. **Substitute the values into the formula:**
- Now, substituting the values of \( r \) and \( h \):
\[ A = 2 \pi (1) (40) = 80 \pi \text{ m}^2 \]

5. **Conclusion:**
- The area of the iron sheet required is \( 80 \pi \text{ m}^2 \).

### Final Answer:
The area of iron sheet required is \( 80 \pi \text{ m}^2 \), which corresponds to option (c).