The curved surface area of a cylinder is 528 square centimetres. If the circumference of its base is 44 cm, what is the height of the cylinder?

Introduction / Context:
This question involves a right circular cylinder and asks for its height when the curved surface area and the base circumference are given. The curved surface area can be expressed as the product of the circumference of the base and the height. This gives a very direct way to find the height when those two quantities are known. It is a classic mensuration question that tests understanding of formulas relating lateral area and circumference for cylinders.

Given Data / Assumptions:
- Curved surface area (CSA) of the cylinder = 528 square centimetres. - Circumference of the base = 44 centimetres. - Height of the cylinder is h centimetres. - Relationship used: CSA = circumference of base * height.

Concept / Approach:
For a cylinder of radius r and height h, the curved surface area is given by CSA = 2 * π * r * h, and the circumference of the base is C = 2 * π * r. Notice that CSA can be written as C * h. In this question, since CSA and C are both given, we can find the height h simply by dividing CSA by C. This avoids any need to work out the radius explicitly.

Step-by-Step Solution:
Step 1: Recall the relationship CSA = circumference * height for a cylinder. Step 2: We are given CSA = 528 square centimetres. Step 3: We are also given circumference C = 44 centimetres. Step 4: Using CSA = C * h, we have 528 = 44 * h. Step 5: Solve for h by dividing both sides by 44: h = 528 / 44. Step 6: Compute 528 / 44 = 12. Step 7: Therefore the height of the cylinder is 12 centimetres.

Verification / Alternative check:
To verify, we can deduce the radius from the circumference C = 44. Since C = 2 * π * r, and with π approximated as 22 / 7, we get 44 = 2 * (22 / 7) * r = (44 / 7) * r, so r = 7 cm. Then CSA = 2 * π * r * h = 2 * (22 / 7) * 7 * 12 = 2 * 22 * 12 = 528 square centimetres, which matches the given curved surface area. This confirms that h = 12 cm is correct.

Why Other Options Are Wrong:
Option 24 cm would require CSA = 44 * 24 = 1056 square centimetres, which does not match the given 528. Option 36 cm would give CSA = 44 * 36 = 1584 square centimetres, far larger than given. Option 6 cm would give CSA = 44 * 6 = 264 square centimetres, which is only half of the required area.

Common Pitfalls:
A common mistake is to try to use π explicitly and compute r first, which is more work and introduces extra chances for arithmetic errors. Another error is mixing up formulas for total surface area and curved surface area. Remember that here total surface area would add the areas of the two circular bases, which is not needed. Simply recognising CSA = circumference * height leads to a quick and clean solution.

Final Answer:
The height of the cylinder is 12 cm.