Q1 of 44 Page 14

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.

Radius of 1st cylindrical vessel = 15cm


and height = 25cm


Radius of 2nd cylindrical vessel = 10cm


and height = 18cm


So, Volume of 1st cylindrical vessel = πr2h


= π × (15)2 × 25


= 5625π cm3


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


= Volume of the third cylindrical Vessel


⇒ 5625π + 1800π = 30πR2


⇒ 7425π = 30πR2



⇒ R2 = 247.5


⇒ R = 15.73cm


Hence, radius of the required cylinder is 15.73cm


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