Explanation:

Let's take radius = r & height = h before incremented volume of cylinder
So volume of cylinder
v = π r² h
Now, after increment
New radius R = 10% of r i.e. R = (r × 10)/100
and H = 20% of h i.e. H = (h × 20)/100
New volume
V = π R² H
= π ((r × 10)/100)² ((h × 20)/100)
= (π r² h) × ((10/100)² × (20/100))
But π r² h = v
So,
V = v × ((100 × 20)/(10000 × 100))
= v × 2/1000
V = v × 0.002