Question

A sphere of diametre 12 cm is dropped into a cylinderical vessal filled with water.if the sphere is completely submerged in water the water level is the cylindrical vessal rises
$3 \frac{5}{9?}$
cm. find the diameter of the cylindrical vessal

Answer 1

Given, diameter of the vessel = 12 cm

So, radius of the vessel = 12/2 = 6 cm

Now, volume of the sphere = (4/3)π r3

= (4/3)π*63

= (4/3)π*6*6*6

= 4*π*6*6*2

= 288π

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

Given, level of the water increased h = 3 (5/9) = 32/9

The shape of the given to be cylindrical.

Let r is the radius of the cylinder.

Now, volume of the water displaced = 288π

=> π r2 h= 288π

=> r2 * 32/9= 288

=> r2 = (288*9)/32

=> r2 = 9*9

=> r2 = 81

=> r = √81

=> r = 9

Hence diameter of the cylinder = 2r = 2*9 = 18 cm