The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. The ratio of their volumes is

The volume of a cylinder is V = πr²h. Since π cancels in a ratio, the volume ratio is (r₁²h₁) : (r₂²h₂). Here r₁:r₂ = 2:3 and h₁:h₂ = 5:3, so the volume ratio is (2²×5) : (3²×3) = 20 : 27. Option B is correct.

Why the others fail:

• A (10:17) does not come from any correct use of the formula. It only appears if you treat the radius as linear, which gives 2×5 : 3×3 = 10:9, and that is not in the options either.
• C (17:27) has no clean derivation from r²h. The denominator 27 is right, but the numerator is wrong.
• D (20:37) gets the numerator right but the denominator wrong. 3²×3 is 27, not 37.

The core concept is that volume depends on the square of the radius and on the first power of the height. Doubling the radius quadruples the volume, while doubling the height only doubles it. This is the same logic used in scaling problems in mensuration and in estimating material needs for tanks, pipes and silos, which is a useful Mains angle when discussing infrastructure cost estimation.

Trap: Aspirants often square the height too, or forget to square the radius. Always square only the radius.