Question

The radius and height of a cylinder are in the ratio 3 : 2 and its volume is 19,404 cm³. Find its radius and height.

Answer 1

The radius and height of a cylinder are in the ratio 3 : 2.

Let the radius be 3x and height be 2x. Then,

Volume of a cylinder = 19404 cm³  ...[Given]

∵  Volume of a cylinder = πr²h

∴ `19404 = 22/7 xx (3x)^2 xx (2x)`

⇒ `19404 = 22/7 xx 9x^2 xx 2x = (22 xx 18x^3)/7`

⇒ `19404 = (396x^3)/7`

⇒ x³ = 343

⇒ x³ = (7)³

∴ x = 7 cm

Hence, radius of the cylinder = 3 × 7 = 21 cm

And height of the cylinder = 2 × 7 = 14 cm