Question

The diameter of cylindrical vessel is 12 meter .the vessel contained some water . a solid sphere of diameter 6 cm is put in the water ,which increased the water level in the vessel .calculate the increase in the water level

Answer 1

Given, the diameter of sphere = 6 cm

⇒ radius of sphere = R = 6/2 = 3 cm

And  diameter of cylindrical vessel = 12 cm.

⇒ radius of cylindrical vessel = r = 12/2 = 6 cm.

Now, volume of sphere = (4/3)πR3

⇒ (4/3)π(3)3

and volume of cylindrical vessel = πr2h = π(6)2h.

Here, the volume of sphere is equal to the volume increased in the cylindrical vessel.

∴  (4/3)π(3)3 =  π(6)2h

h = (4x3x3x3)/(3x6x6) = 1 cm.

Therefore , 1 cm level of water rise in the cylindrical vessel.