Question

A Vessel Is In The Form Of An Inverted Cone.Its Height Is 8cm And The Radius Of Its Top Which Is Open Is 5cm .It Is Filled With Water Up To The Brim. When Lead Shots Each Of Which Is A Sphere Of Radius 0.5cm Are Dropped Into The Vessel One-Fourth Of The Water Flows Out.Find The Number Of Lead Shots Dropped In The Vessel.

Answer 1

Step-by-step explanation:

volume of cone=1/3πr$r^{2}$h

                         =1/3×π×$5^{2}$×8

                         =25×8π×1/3

                         =200π/3 cubic cm

volume of lead shots =4/3×π×0.5×0.5×0.5

                                   =4/3×π×0.125

                                   =5π/30

                                   =1π/6

                                   =π/6 cubic cm

volume displaced by  =1/4×π×200/3

each lead shot              

                                    =50π/3π cubic cm

let the no.of lead shots to be displaced =n

n×π/6=50π/3

n/6=50/3(by cancelling π on both sides)

n=50/3×6

n=100

therefore,100 lead shots can displace the water in the vessels.