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Question

A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the volume of water (i) displaced out of the cylinder (ii) left in the cylinder.

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Solution

We have,

Internal radius of the cylindrical vessel, R = 10/2= 5 cm,

Height of the cylindrical vessel, H = 10.5 cm,

Radius of the solid cone, r = 72 = 3.5 cm and

Height of the solid cone, h = 6 cm

(i) Volume of water displaced out of the cylinder = Volume of the solid cone

= 13πr2h

= 13×227×3.5×3.5×6
= 77 cm3

(ii) As, Volume of the cylindrical vessel = πR2H

= 227×5×5×10.5

= 825 cm3

So, the volume of water left in the cylindrical vessel = Volume of the cylindrical vessel -Volume of the solid cone

= 825 - 77 = 748 cm3


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