The curved surface area of a right circular cylinder is 1232 square centimetres. If the circumference of its circular base is 154 centimetres, what is the height of the cylinder? (Take π = 22/7.)

Introduction / Context:
This problem focuses on the relationship between the curved surface area of a right circular cylinder, the circumference of its base and its height. Cylinders occur frequently in practical applications, such as tanks, pipes and cans, so curved surface area and circumference formulas are widely used in aptitude and engineering questions.

Given Data / Assumptions:
- Curved surface area (CSA) of the cylinder = 1232 square centimetres.
- Circumference of the base = 154 centimetres.
- The cylinder is right circular, so the axis is perpendicular to the base.
- Take π = 22 / 7 as directed in the question.
- We must find the height h of the cylinder in centimetres.

Concept / Approach:
For a right circular cylinder, the curved surface area is given by:
CSA = 2 * π * r * h
The circumference of the base is given by:
Circumference = 2 * π * r
A very useful shortcut is that the curved surface area can also be written as:
CSA = (circumference of base) * height
In this question, we already know the curved surface area and the circumference. So we can simply divide CSA by the circumference to get the height directly.

Step-by-Step Solution:
Step 1: Use the relation CSA = circumference * height. Step 2: Substitute the given values: 1232 = 154 * h. Step 3: Solve for h by dividing both sides by 154. Step 4: h = 1232 / 154. Step 5: Compute 1232 / 154 = 8, so the height of the cylinder is 8 cm.

Verification / Alternative check:
We can double check by starting with the standard formulas. From the circumference 2 * π * r = 154, using π = 22 / 7, we get r = 154 / (2 * 22 / 7) = 154 * 7 / 44 = 24.5 cm. Then the curved surface area formula 2 * π * r * h should equal 1232. Substituting r = 24.5 and h = 8, we get 2 * 22 / 7 * 24.5 * 8 = 1232, confirming that the height is correct.

Why Other Options Are Wrong:
Heights 4 cm, 6 cm, 12 cm and 16 cm would all give either too small or too large a curved surface area when multiplied by the given circumference 154 cm. None of them satisfy the exact relation 154 * h = 1232 except h = 8 cm.

Common Pitfalls:
Many students first try to compute the radius from the circumference formula and then go back to the curved surface area formula. Although this works, it takes more time and increases the chance of arithmetic mistakes. Another common error is confusing total surface area with curved surface area. In this question, only the curved surface area is relevant, so the simple product circumference times height is enough.

Final Answer:
The height of the cylinder is 8 cm.