Question

A sphere of diameter 6cm is dropped into a circular cylindrical vessel partly filled with water. The diameter of the vessel is 12cm . If the sphere is completely submerged in water the rise in the level of water in the vessel is ____ cm

Answer 1

Hi ,

1 ) diameter of the sphere ( d ) = 6cm

     radius of the sphere ( r ) = d/2 = 6/2 = 3cm

2 ) diameter of the cylindrical vessel ( D ) = 12 cm

radius of the cylindrical vessel ( R ) = 12/2 = 6 cm

level of water raised = h cm

according to the problem given ,

volume of the water raised in the vessel = volume of the sphere

πR²h = 4/3 × πr³

h = ( 4 × r³ ) / ( 3 × R² )

h = ( 4 × 3 × 3 × 3 ) / ( 3 × 6 × 6 )

h = 1 cm

Therefore ,

level of water raised in the vessel = h = 1 cm

I hope this helps you.

Answer 2

Answer:

1 ) diameter of the sphere ( d ) = 6cm

    radius of the sphere ( r ) = d/2 = 6/2 = 3cm

2 ) diameter of the cylindrical vessel ( D ) = 12 cm

radius of the cylindrical vessel ( R ) = 12/2 = 6 cm

level of water raised = h cm

according to the problem given ,

volume of the water raised in the vessel = volume of the sphere

πR²h = 4/3 × πr³

h = ( 4 × r³ ) / ( 3 × R² )

h = ( 4 × 3 × 3 × 3 ) / ( 3 × 6 × 6 )

h = 1 cm