The area of the curved surface of a right circular cylinder is 4400 cm² and…
2024
The area of the curved surface of a right circular cylinder is 4400 cm² and the circumference of its base is 110 cm. Its volume (in m³) is : (Use π = 22/7)
Answer: B. 0.0385 — For a right circular cylinder of base radius r and height h, the base circumference is 2πr, the curved surface area (CSA) equals the base circumference…
- A.
0.0284
- B.
0.0385
- C.
0.0285
- D.
0.0382
Show answer & explanation
Correct answer: B
For a right circular cylinder of base radius r and height h, the base circumference is 2πr, the curved surface area (CSA) equals the base circumference multiplied by the height, i.e. CSA = 2πrh, and the volume is V = πr2h.
Find the radius from the base circumference: 2πr = 110 cm, so r = 110 ÷ (2 × 22/7) = 17.5 cm.
Find the height from the curved surface area: CSA = circumference × h, so 4400 = 110 × h, giving h = 40 cm.
Compute the volume: V = πr2h = (22/7) × (17.5)2 × 40 = 38500 cm3.
Convert to cubic metres: since 1 m3 = 1,000,000 cm3, V = 38500 ÷ 1,000,000 = 0.0385 m3.
Cross-check: substituting r = 17.5 cm back into the circumference formula gives 2πr = 2 × (22/7) × 17.5 = 110 cm, and CSA = 110 × 40 = 4400 cm2, both matching the values given in the question, which confirms the volume 0.0385 m3.