A cylindrical rod has an outer curved surface area of 8100 cm2. If its length…
2026
A cylindrical rod has an outer curved surface area of 8100 cm2. If its length is 89 cm, what is its outer radius, rounded to two decimal places? Take π = 22/7.
Answer: B. 14.48 — ConceptFor a cylinder, the curved surface area is the circumference of the circular base multiplied by the cylinder’s length. Thus, CSA = 2πrh. When CSA and…
- A.
17.79
- B.
14.48
- C.
12.71
- D.
17.93
Attempted by 12 students.
Show answer & explanation
Correct answer: B
Concept
For a cylinder, the curved surface area is the circumference of the circular base multiplied by the cylinder’s length.
Thus, CSA = 2πrh. When CSA and height h are known, isolate the radius using r = CSA/(2πh).
Application
Substitute CSA = 8100 cm2, h = 89 cm, and π = 22/7 into r = CSA/(2πh).
r = 8100/[2 × (22/7) × 89] = (8100 × 7)/(44 × 89).
r = 56700/3916 = 14.479060… cm.
Rounding to two decimal places gives r = 14.48 cm.
Cross-check
Using r = 14.48 cm, 2πrh = 2 × (22/7) × 14.48 × 89 ≈ 8100.53 cm2, which is 8100 cm2 to the precision implied by the rounded radius.