A cylinder, opened at one end, has a radius of 3.5cm and height 8cm. calculate the total surface area

Analyze the question: The cylinder is open at one end, so it has a curved side and only one circular base (no top).

Concept: Total surface area (open at one end) = curved surface area + area of one circle = 2πrh + πr²

Solution: Use π = 22/7, r = 3.5 cm, h = 8 cm.

1. Curved surface area = 2πrh = 2 × (22/7) × 3.5 × 8 = 2 × 22 × 0.5 × 8 = 176 cm²

2. Base area = πr² = (22/7) × 3.5 × 3.5 = 22 × 0.5 × 3.5 = 38.5 cm²

3. Total = 176 + 38.5 = 214.5 cm²

Check against the options: 214.5 cm² matches option D.

(If you had wrongly used both ends, you would get 176 + 77 = 253 cm², which is not an option. That confirms the "open at one end" reading.)

Tip: Always read the wording "open at one end" or "closed". Open at one end means 2πrh + πr². Closed at both ends means 2πrh + 2πr². Also, when r = 3.5, use π = 22/7 because 3.5 = 7/2 cancels neatly.