Question

a conical vessel of radius 14 cm and height 7 cm is full of water. a sphere is dipped into it and it completely gets immersed making 1/8th part of the water splash out of the vessel. what is the radius of the sphere?

Answer 1

Given:-
radius of cone = 14 cm 
height of cone = 7cm 
volume of cone = πr2h
                        = πr2h
                        = π*14*14*7
                        =22*14*14 
                       = 4312 cm3
volume of water splashed out = volume of sphere
volume of water splashed out = 1/8πr2h
volume of water splashed out = 4312/8
volume of water splashed out = 539 cm2
volume of sphere                   = 4/3*πr​3
volume of sphere                   = 4/3*πr​3= 539
                                            r3  = 539/π*3/4
                                            r3  = 343/2*3/4
                                             r3 = 1029/8
                                             r  =3.5 √3 
                                        r = 3.5*1.73
            radius of sphere  = 6.05 cm