Cylinders — Radii in ratio 2:3 and heights in ratio 5:3. Find the ratio of their volumes.

Introduction / Context:
Volume of a cylinder V = π r^2 h. Ratios multiply across exponents: r contributes squared, h contributes linearly.

Given Data / Assumptions:

• r1:r2 = 2:3
• h1:h2 = 5:3

Concept / Approach:
Compute V1:V2 = (r1^2 h1):(r2^2 h2) = (2^2 * 5) : (3^2 * 3).

Step-by-Step Solution:
V1:V2 = (4 * 5):(9 * 3) = 20:27

Verification / Alternative check:
Plug sample values (e.g., r1=2, r2=3, h1=5, h2=3) to confirm the computed ratio.

Why Other Options Are Wrong:
27:20 inverts; 4:9 or 9:4 ignore heights; 5:3 ignores r^2.

Common Pitfalls:
Forgetting to square the radius in volume formula.

Final Answer:
20 : 27