Question

integer.
32. A conical vessel of radius 8 cm and be
15 cm is completely filled with water
sphere is lowered into the water and its size
is such that when it touches the sides, it is
just immersed as shown in the figure. What
fraction of water overflows?​

Answer 1

≡QUESTION≡

A conical vessel of radius 8 cm and be  15 cm is completely filled with water

sphere is lowered into the water and its size  is such that when it touches the sides. What  fraction of water overflows?​

                                                                                       

║⊕ANSWER⊕║

Let say radius of Sphere = r

Volume of Cone = Volume of Water

                            = (1/3)π(8)² * 15

                             = 320π cm³

Slant height = √8² + 15²

                     = √289

                       = 17 cm

Sinθ = 8/17   (in Δ  POR)

Sinθ = OM/OR   ( (in Δ  MOR)

OM = radius of sphere = r

OR = 15 - r

=> r/(15 - r)  = 8/17

=> 17r = 120 - 8r

=> 25r = 120

=> r = 4.8 cm

Volume of sphere = (4/3)π r³  

                               =  (4/3)π (4.8)³

                                = 147.456 π cm³

Volume of Water over flow = 147.456 π cm³

Fraction of water overflows = 147.456 π / 320π

                                                = 0.4608

                                                = 4608/10000

                                                = 0.4608 cm³