A rectangular piece of paper measuring 11 cm × 4 cm is rolled without overlap…
2026
A rectangular piece of paper measuring 11 cm × 4 cm is rolled without overlap to form a cylinder of height 4 cm. Find the cylinder’s volume. Use π = 22/7.
Answer: D. 38.5 cm3 — ConceptWhen a rectangle is rolled into a cylinder without overlap, the side that closes around the circular base becomes its circumference, while the other…
- A.
18.5 cm3
- B.
33.5 cm3
- C.
35.5 cm3
- D.
38.5 cm3
Attempted by 4 students.
Show answer & explanation
Correct answer: D
Concept
When a rectangle is rolled into a cylinder without overlap, the side that closes around the circular base becomes its circumference, while the other side becomes the height. For a cylinder, C = 2πr and V = πr2h.
Application
Here the 11 cm side forms the circumference and the 4 cm side is the height, so 2πr = 11.
Therefore r = 11/(2π) = 11/[2 × (22/7)] = 7/4 cm.
Now V = πr2h = (22/7) × (7/4)2 × 4 = 38.5 cm3.
Cross-check
The cylinder’s curved surface area is 2πrh = 2 × (22/7) × (7/4) × 4 = 44 cm2, equal to the paper’s area 11 × 4 = 44 cm2. Thus the folding dimensions are consistent.
Therefore, the volume of the cylinder is 38.5 cm3.