Question

A sphere of diameter 12 cm, is dropped in a 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 3/5/9mixed fraction cm. Find the diameter of the cylindrical vessel.

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
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