A hollow right circular cylinder is open at both ends. Its length is 22 cm, the external radius is 7 cm, and the wall thickness is 1 cm. Using π = 22/7, what is the total surface area of this hollow cylinder in square centimetres?

Introduction / Context:
This question tests the concept of total surface area of a hollow right circular cylinder that is open at both ends. Many competitive exams include such problems to check whether students correctly combine curved surface areas and ring shaped end areas, and whether they correctly handle internal and external radii when the cylinder is hollow.

Given Data / Assumptions:
- The cylinder is hollow and open at both ends.
- Length or height h = 22 cm.
- External radius R = 7 cm.
- Wall thickness t = 1 cm, so internal radius r = R − t = 6 cm.
- Use π = 22/7 as given.

Concept / Approach:
For a hollow cylinder open at both ends, total surface area includes four parts:
- Outer curved surface area = 2 * π * R * h.
- Inner curved surface area = 2 * π * r * h.
- Area of the two circular rings at the ends = 2 * π * (R^2 − r^2).
Total surface area = 2 * π * h * (R + r) + 2 * π * (R^2 − r^2).

Step-by-Step Solution:
Step 1: Compute R + r = 7 + 6 = 13 cm. Step 2: Compute R^2 − r^2 = 7^2 − 6^2 = 49 − 36 = 13. Step 3: Outer plus inner curved area = 2 * π * h * (R + r) = 2 * (22/7) * 22 * 13. Step 4: Simplify curved area: 2 * (22/7) * 22 * 13 = (44/7) * 22 * 13 = (968/7) * 13 = 12584/7. Step 5: Area of both ring shaped ends = 2 * π * (R^2 − r^2) = 2 * (22/7) * 13 = 572/7. Step 6: Total surface area = 12584/7 + 572/7 = 13156/7 sq.cm. Step 7: 13156/7 = 1879.428571..., which rounds to 1879.43 sq.cm.

Verification / Alternative Check:
A quick check is to compute curved and end areas separately using approximate decimal π. With π close to 3.14 the result remains near 1880 sq.cm, which agrees with the more exact fraction based value, confirming the correctness of the calculation and the chosen formula structure.

Why Other Options Are Wrong:
Option b, 3758.86 sq.cm, is almost exactly double the correct answer and would arise if someone incorrectly doubled the entire total surface expression.
Option c, 939.715 sq.cm, is about half the correct result and could come from using only curved surfaces or only one side of the cylinder.
Option d, 2819.145 sq.cm, does not match any proper combination of inner and outer surfaces and most likely comes from mixing radii or omitting one component of area.

Common Pitfalls:
Common mistakes include treating the hollow cylinder as solid, forgetting to include inner curved surface area, or ignoring the ring shaped end areas. Students sometimes use only one radius instead of both internal and external radii, or forget that the cylinder is open at both ends and either add or remove the wrong circular areas. Carefully listing all contributing surface parts avoids such errors.

Final Answer:
The total surface area of the hollow cylinder is 1879.43 sq.cm.