Question

A sphere of diameter 5 cm is dropped into a cylindrical vessel partly filled with water. If sphere is completely submereged and water incylinder rises by 32/9 cm .Find diameter of vessel

Answer 1

Answer:

Step-by-step explanation:

Given, diameter of the vessel = 5 cm

So, radius of the vessel = 5/2 = 2.5 cm

Now, volume of the sphere = (4/3)π r3

= (4/3)π*2.53

= (4/3)π*2.5*2.5*2.5

= 20.83π

Now, water displaced is equal to the volume of the sphere

Given, level of the water increased h = 32/9

The shape of the given to be cylindrical.

Let r is the radius of the cylinder.

Now, volume of the water displaced = 20. 83π

=> π r2 h= 20.83π

=> r2 * 32/9= 20.83

=> r2 = (20.83*9)/32

=> r2 = 187.47/32

=> r2 = 5.8584375

=> r = √5.8584375

=> r = 2.4204209345

Hence diameter of the cylinder = 2r = 2*2.4204209345

=4.8408418689 cm