One hundred fifty spherical marbles, each of 14cm, are dropped in cylindrical vessel of diameter 7cm containing some water and are completely immersed in water. Find the rise in the level of water in the vessel.
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Answer:
Diameter of the spherical marble =1.4 cm
Radius of the marble =0.7 cm
Volume of each marble = 34πr3=34×722×(0.7)3=1.44
Volume of 150 marbles =1.44x150=216 cm3
Let the rise in level of water in the cylindrical vessel =h cm
Diameter of the vessel =7 cm
Radius of the vessel =3.5 cm
Volume of increased level of the water = πr2h=722×3.52×h
Volume of increased level of the water = Volume of 150 marbles
722×3.52×h=216
h=5.6 cm
Therefore, the rise in the level of water in the vessel =5.6 cm.
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