Question

. A sphere of diameter 12 cm, is dropped in
right circular cylindrical vessel, partly
filled with water. If the sphere is completely
submerged in water, the water level in the
cylindrical vessel rises by 32/9 cm. Find thediameter of the cylindrical vessel.​

Answer 1

Answer: Diameter of the cylindrical Vessel is 18 cm

Step-by-step explanation:

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

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