Let, radius of cylinder = r and the height of cylinder = 2r

If its height be 7 times its diameter, new height of cylinder = 14r

Case – 1: Volume = 1\over 3 2πr²h

= 1\over 3 × 2 × 22\over 7 × r² × 2r

= 44r³\over 21

Case – 2:  Radius = r, Height = 14r

Volume = 1\over 3 πr²h

= 1\over 3 × 2 × 22\over 7 × r² × 14r

= 308r³\over 21

According to the Question,

14\over 3 × πr³ – 2\over 3 × πr³ = 539

or, 4πr³ = 539

or, 4 × 22\over 7 × r³ = 539

or, r³ = 539 × 7\over 22 × 4

or, r³ = 7 × 7 × 7 \over 2 × 2 × 2

or, r = 7\over 2 = 3.5 cm

Given Height is twice of the radius,

H = r × 2 = 3.5 × 2 = 7 cm