Question

Two cylindrical vessels are filled with oil. The radius of one vessel is 15 cm and its height is 25 cm. The radius and height of the other vessel are 10cm and 18 cm respectively. Find the radius of a cylindrical vessel 30 cm in height, which will just contain the oil of two given vessels.

Answer 1

Radius of 1^st cylindrical vessel = 15cm

and height = 25cm

Radius of 2^nd cylindrical vessel = 10cm

and height = 18cm

So, Volume of 1^st cylindrical vessel = πr²h

= π × (15)² × 25

= 5625π cm³

Volume of 2^nd cylindrical vessel = π(r’)²h’

= π × (10)² × 18

= 1800π cm³

Height of the third vessel = 30cm

and let its radius be R

So,

Volume of third cylindrical vessel = πR²H

= πR²×30

= 30πR²

Volume of 1^st cylindrical vessel + Vol. of 2^nd Cylindrical vessel

= Volume of the third cylindrical Vessel

⇒ 5625π + 1800π = 30πR²

⇒ 7425π = 30πR²

⇒ 7425/30 = R²

⇒ R² = 247.5

⇒ R = 15.73cm

Hence, radius of the required cylinder is 15.73cm