Question

The radius of a solid right circular cylinder increases by 20% and the height decreases by 10%. Find the percentage change in the volume.

Answer 1

Given:

Let the original radius = r and height = h.

Volume formula: V = π r² h.

New radius = 1.20r (increase 20%)

new height = 0.90h (decrease 10%)

New volume: V = π(1.20r)²(0.90h)

= πr² h × (1.20² × 0.90) 

= V × 1.296

Percentage change = `(V' − V)/V × 100%`

= (1.296 − 1) × 100%

= 29.6%