The volume of a right circular cylinder of length 1.2 metres is 4620 cm³. What…

Concept

For a right circular cylinder of radius r and height h, the volume is V = πr2h, and the curved (lateral) surface area is CSA = 2πrh. The plan is to use the given volume and height to find the radius, then substitute that radius and height into the CSA formula.

Application

1. Convert the height to consistent units: length 1.2 m = 1.2 × 100 = 120 cm, so h = 120 cm.

2. Use the volume to find r2: πr2h = 4620, i.e. (22/7) × r2 × 120 = 4620.

3. Solve for r2: r2 = (4620 × 7) ÷ (22 × 120) = 32340 ÷ 2640 = 12.25, so r = √12.25 = 3.5 cm.

4. Compute the curved surface area: CSA = 2πrh = 2 × (22/7) × 3.5 × 120 = 2 × 22 × 0.5 × 120 = 2640 cm2.

Cross-check

Substitute r = 3.5 cm back into the volume: πr2h = (22/7) × 12.25 × 120 = 4620 cm3, which matches the given volume — confirming r = 3.5 cm and a curved surface area of 2640 cm2.