Geometry and TrigonometryHardLabel area on a can
Geometry and Trigonometry practice question
A cylindrical can has a radius of 5 centimetres and a height of 10 centimetres. A paper label covers the curved side of the can exactly, with no overlap. What is the area of the label, in square centimetres?
- A. 100πCorrect
- B. 50π
- C. 250π
- D. 150π
Answer: A. 100π
The curved side unrolls into a rectangle whose width is the circumference, 2π(5) = 10π, and whose height is 10. Area: 10π × 10 = 100π.
Why the other answers are wrong
- B. 50π
- 50π uses the radius instead of the diameter in the circumference (π × 5 × 10).
- C. 250π
- 250π is πr²h, the VOLUME.
- D. 150π
- 150π adds the two circular ends (2 × 25π), but the label covers only the side.
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