Question

Sphere of diameter 12 cm is dropped in a right circular cylindrical vessel, partly filled with water. The diameter of the cylindrical vessel is 24 cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?

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.

: )