A cylindrical tube, which is open at both ends, is crafted from a metal. The internal diameter of the tube is 12 cm, and its length is 35 cm. The metal throughout has a thickness of 2 cm. Determine the total surface area (in cm²) of the metal tube.
Take π = 22/7
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e 3256.
Internal diameter = 12 cm → Internal radius (r₁) = 6 cm
Thickness = 2 cm → External radius (r₂) = 6 + 2 = 8 cm
Outer curved surface area = 2 × π × r₂ × h = 2 × (22/7) × 8 × 35 = 2 × (22 × 8 × 5) = 2 × 880 = 1760 cm²
Inner curved surface area = 2 × π × r₁ × h = 2 × (22/7) × 6 × 35 = 2 × (22 × 6 × 5) = 2 × 660 = 1320 cm²
Surface area of the two circular rings (ends) = π × (r₂² - r₁²) = (22/7) × (64 - 36) = (22/7) × 28 = 88 cm²
For two ends: 2 × 88 = 176 cm²
Total surface area = 1760 + 1320 + 176 = 3256 cm²