Find cylinder height from total surface area: A solid cylinder has radius 5 cm and total surface area 660 cm^2. Compute its height h (in cm).

Introduction / Context:
Total surface area (TSA) for a cylinder equals the curved surface area plus the areas of both circular ends. Given TSA and radius, we can isolate height by algebra. This tests formula fluency and neat handling of π in denominators.

Given Data / Assumptions:

• r = 5 cm
• TSA = 660 cm^2
• TSA formula: 2πr(h + r)

Concept / Approach:
Solve 2πr(h + r) = 660 for h. Keep the algebra symbolic until the last step to avoid rounding drift; then evaluate numerically with π ≈ 3.14 (or 22/7) and round to a listed option.

Step-by-Step Solution:
2πr(h + r) = 660 → 10π(h + 5) = 660h + 5 = 660 / (10π) = 66 / πUsing π ≈ 3.14 → h + 5 ≈ 21.019 → h ≈ 16.019 cm ≈ 16 cm

Verification / Alternative check:
Plug h = 16 into TSA: 2π * 5 * (16 + 5) = 10π * 21 = 210π ≈ 659.73 cm^2, which rounds to 660 cm^2.

Why Other Options Are Wrong:
10, 12, 14, 15 cm give TSA values significantly apart from 660 cm^2 when substituted into the formula; 16 cm uniquely satisfies the equation within rounding.

Common Pitfalls:
Using curved area 2πrh in place of TSA; forgetting both ends; arithmetic slips when dividing by π.

Final Answer:
16 cm