Let the radius of the base and height of the cylinder be 5x cm and 7x cm respectively.
Then,
Volume = 550 cm^{3}
⇒ 22/7 × (5x)^{2 } × 7x = 550 [Use, r = 5x; h = 7x and volume = πr^{2}h]
⇒ 22/7 × 25x^{2} × 7x = 550
⇒ 22 × 25x^{3} = 550
⇒ 550x^{3} = 550
⇒ x^{3} = 1
⇒ x = 1 cm
Hence, radius of the cylinder
= 5x cm = (5 × 1) cm
= 5 cm.