Question

the radius and height of a cylinder are in ratio 5 is to 7 and its volume is 550 cm cube find its radius


the thickness of hollow metallic cylinder is it is 35 cm long and its inner radius is 12 cm find the volume of metal required to make the cylinder assuming it is open, at either end​

Answer 1

GIVEN :-

The ratio between the radius and the height of the cylinder is 5 : 7

Let the radius and height of the cylinder be 5x and 7x respectively.

volume of the cylinder is given = 550cm³

we know that,

πr²h = volume of a cylinder

⇒ πr²h = 550cm³

⇒ 22/7 * (5x)² * 7x = 550cm³

⇒ 22 * 25x³ = 550cm³

⇒ 550x³ = 550cm³

⇒ x³ = 550/550

⇒ x³ = 1

⇒ x = ³√1

⇒ x = 1cm

hence,

• radius of the cylinder = 5x = 5cm

• height of the cylinder = 7x = 7cm

VERIFICATION :-

volume of the cylinder = πr²h

= 22/7 × 5 × 5 × 7

= 22 × 25

= 550cm³ hence verified!