A cylindrical metallic barrel of height 2.5m and radius 0.245 is closed at one end. Find, correct to one…

Analyze the question: The barrel is a cylinder closed at one end only, so it has one circular base plus the curved surface. The radius is written as 0.245 with no unit, so we take it as 0.245 m.

Concept: Total surface area (closed at one end) = curved surface area + one circular base = 2πrh + πr² = πr(2h + r)

Solution: Using π = 22/7, r = 0.245, h = 2.5:

1. Curved surface area = 2πrh = 2 × (22/7) × 0.245 × 2.5 • 0.245 × 2.5 = 0.6125 • 2 × (22/7) × 0.6125 = (44/7) × 0.6125 = 3.85 m²

2. Base area = πr² = (22/7) × 0.245 × 0.245 • 0.245² = 0.060025 • (22/7) × 0.060025 = 0.18865 m²

3. Total = 3.85 + 0.18865 = 4.03865 m² ≈ 4.0 m² (1 d.p.)

Check with the other options: If both ends were closed, the total would be 3.85 + 2(0.18865) ≈ 4.23 ≈ 4.2 m², which is not an option. The curved surface alone is 3.85 ≈ 3.9 m², which is also not an option. So 4.0 m² fits the "closed at one end" condition.

Answer: C. 4.0 m²

Tip: Read the wording on how many ends are closed.

• Open at both ends → 2πrh
• Closed at one end → 2πrh + πr²
• Closed at both ends → 2πrh + 2πr²

Also, 0.245 × 7 = 1.715, which is handy for cancelling the 7 in 22/7 quickly.