Cost to paint the curved surface of a cylindrical pillar: A pillar of diameter 50 cm (radius 0.25 m) and height 3.5 m is painted on its curved surface at ₹ 10 per m^2. Find the cost.

Introduction / Context:
Painting the curved surface of a cylinder uses the lateral area 2πrh. Multiply the area by the rate to get the total cost. This exercise checks unit conversion and correct identification of “covered surface” as the curved area only.

Given Data / Assumptions:

• Diameter = 0.50 m → r = 0.25 m
• Height h = 3.5 m
• Rate = ₹ 10 per m^2
• Curved area A = 2πrh

Concept / Approach:
Compute A first, then multiply by rate. Use π ≈ 3.14 (or 22/7) for a numeric amount in rupees; round to the nearest rupee if needed.

Step-by-Step Solution:
A = 2πrh = 2 * π * 0.25 * 3.5 = 1.75π m^2Using π ≈ 3.14 → A ≈ 5.495 m^2Cost = 5.495 * ₹ 10 ≈ ₹ 54.95 ≈ ₹ 55

Verification / Alternative check:
Using π = 22/7 gives A = 1.75 * (22/7) = 5.5 m^2 → cost ₹ 55 exactly. Both calculations agree within rounding.

Why Other Options Are Wrong:
₹ 50 and ₹ 60 bracket the correct value but are off; ₹ 68 and ₹ 98 are too large given the modest area; ₹ 55 uniquely matches the computation.

Common Pitfalls:
Including top/bottom surfaces (not asked); leaving diameter instead of radius in 2πrh; forgetting to convert 50 cm to meters when needed.

Final Answer:
₹ 55