Geometry and TrigonometryVery hardTotal surface area of a closed cylinder
Geometry and Trigonometry practice question
A closed right circular cylinder has a radius of 3 and a height of 7. What is its total surface area?
- A. 60πCorrect
- B. 42π
- C. 63π
- D. 51π
Answer: A. 60π
Two circular ends: 2 × π(3²) = 18π. Curved side: circumference × height = 2π(3)(7) = 42π. Total: 18π + 42π = 60π.
Why the other answers are wrong
- B. 42π
- 42π is the curved side alone; a CLOSED cylinder also has two circular ends, 9π each.
- C. 63π
- 63π is π(3²)(7), the VOLUME, not the surface area.
- D. 51π
- 51π counts only one of the two circular ends (9π + 42π). Both ends are there.
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