The radii of two cylinders are in the ratio 1 : 4 and their heights are in the ratio 4: 3. Their volumes will be in the ratio _____.

1 : 12

We know that,

Volume of cylinder = πr²h

Ratio of radius = 1 : 4 

Ratio of Heights = 4 : 3 

1st cylinder, radius = 1a, height = 4b 

2nd cylinder, radius = 4a, height = 3b

Ratio of  their volume(1st : 2nd) = π × (1a)² × 4b : π × (4a)² × 3b  = 4 : 48 = 1 : 12