Q33 of 56 Page 13

The (3/4)th part of a conical vessel of internal radius 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height of water in cylindrical vessel.(CBSE 2017)

Radius of cone = r = 5 cm

Height of cone = h = 24 cm


Volume of cone = (1/3)πr2h


= (1/3) × π × 25 × 24


= 200π cm3


3/4th volume of cone = 3/4 × 200π = 150π cm3


∴ Volume of water in cone = 150 cm3


Radius of cylindrical vessel = R =10 cm


Let height of the cylindrical vessel = H (say)


Volume of water = Volume of cylindrical vessel = πr2h


∴ πR2H = 150π


⇒ R2H = 150


⇒ (10)2H = 150


⇒ 100H = 150


⇒ H = 150/100 = 1.5 cm


∴ Height of the cylindrical vessel = 1.5 cm

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