Find the curved surface area (in square centimetres) of a right circular cylinder whose diameter is 28 cm and height is 12 cm.

Introduction / Context:
This question focuses on the curved surface area (also called lateral surface area) of a right circular cylinder. It checks if you can correctly identify the radius from the diameter and apply the standard formula for curved surface area, which depends on the circumference of the base and the height of the cylinder.

Given Data / Assumptions:

• Diameter of the cylinder = 28 cm.
• Height of the cylinder h = 12 cm.
• Radius r = diameter / 2 = 14 cm.
• We need the curved surface area, not the total surface area.
• Use π in symbolic form or as 22/7 for simple calculation.

Concept / Approach:
The curved surface area (CSA) of a right circular cylinder is given by CSA = 2 * π * r * h. This is equivalent to the product of the circumference of the base and the height. Here, once we identify r = 14 cm and h = 12 cm, we substitute into the formula, simplify using π = 22/7, and obtain the area in square centimetres.

Step-by-Step Solution:
Step 1: Compute the radius: r = 28 / 2 = 14 cm. Step 2: Write the formula for curved surface area of a cylinder: CSA = 2 * π * r * h. Step 3: Substitute r = 14 cm and h = 12 cm: CSA = 2 * π * 14 * 12. Step 4: Multiply 2 * 14 = 28, then 28 * 12 = 336. So CSA = 336π square centimetres. Step 5: Using π = 22/7, CSA = 336 * 22 / 7. Step 6: Simplify 336 / 7 = 48. Therefore CSA = 48 * 22 = 1056. Step 7: The curved surface area is 1056 square centimetres.

Verification / Alternative check:
You can view the curved surface of a cylinder as a rectangle whose one side is the height h and the other side is the circumference of the base, 2πr. Here, circumference = 2 * π * 14 ≈ 2 * 3.14 * 14 ≈ 87.92 cm. Multiplying by the height 12 cm gives an area of about 1055 cm^2, which rounds closely to 1056 when π is taken as 22/7. This matches the exact value obtained using π = 22/7.

Why Other Options Are Wrong:
Values 968, 924, and 856 square centimetres would correspond to different combinations of radius, height, or a misused formula (such as mixing total and curved surface area or using diameter instead of radius directly in the formula). Only 1056 matches the correctly computed curved surface area for r = 14 cm and h = 12 cm.

Common Pitfalls:
Learners often forget to divide the diameter by 2 to get the radius, leading to overestimation by a factor of 4. Another mistake is to confuse curved surface area with total surface area and add the areas of the circular bases unnecessarily. Some also miscalculate 336 * 22 / 7 by not simplifying 336 / 7 first. Taking the steps slowly and checking each arithmetic operation helps avoid these errors.

Final Answer:
The curved surface area of the cylinder is 1056 square centimetres.