Right circular cylinder – total surface area (TSA): A cylinder has base diameter 14 cm (radius 7 cm) and height 40 cm. Find its total surface area (both circular ends + curved surface) in cm^2.

Introduction / Context:
Total surface area (TSA) of a cylinder sums the curved area and the areas of the two circular bases. This tests recall of the TSA formula and careful substitution of radius and height.

Given Data / Assumptions:

• Diameter = 14 cm → r = 7 cm
• Height h = 40 cm
• TSA = 2πr(h + r)

Concept / Approach:
Use the compact TSA identity to avoid computing parts separately. Keep π symbolic until the final step to minimize rounding error, then evaluate numerically to compare with the options.

Step-by-Step Solution:
TSA = 2π * 7 * (40 + 7) = 14π * 47 = 658π cm^2Using π ≈ 3.14 → TSA ≈ 658 * 3.14 ≈ 2066.12 cm^2Using π = 22/7 → TSA = 658 * (22/7) = 94 * 22 = 2068 cm^2

Verification / Alternative check:
Compute parts: curved = 2πrh = 2π * 7 * 40 = 560π; two bases = 2πr^2 = 2π * 49 = 98π; sum = 658π → consistent.

Why Other Options Are Wrong:
1825, 1925, 2050, 2160 do not equal 658π; 2068 matches exactly with π = 22/7, a standard exam convention.

Common Pitfalls:
Using diameter instead of radius in r^2; omitting one base; mixing curved surface area with TSA.

Final Answer:
2068 sq cm