The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.

Problem Restatement

For a cylinder, use CSA = 2πrh and Volume = πr^2h to determine the ratio diameter : height.

Given formulas

• Curved surface area: 2πr h = 264
• Volume: πr^2 h = 924

Concept / Approach

Eliminate h or r using the two equations to find dimensions up to a constant and then form the ratio.

Step-by-step calculation

From volume: πr^2h = 924 → h = 924 ÷ (πr^2)Substitute in CSA: 2πr × [924 ÷ (πr^2)] = 264Simplify: 2 × 924 ÷ r = 264 → 1848 ÷ r = 264 → r = 1848 ÷ 264 = 7Radius r = 7 m → Diameter d = 14 mFind height: πr^2h = 924 → π(49)h = 924 → h = 924 ÷ (49π) ≈ 6Therefore, diameter : height = 14 : 6 = 7 : 3

Check

• CSA = 2πr h = 2&pi(7)(6) = 84π ≈ 264 ✓

Final Answer

Ratio (diameter : height) = 7 : 3.