Question

solid spheres of diameter 4cm. are dropped into a cylindrical beaker containing some water &are fully submerged .if the diameter of beaker is18cm&water rises by 40cm. find the no. of solid spheres dropped in the water

Answer 1

Let the no. of spheres dropped be n

 Initial volume of cylinder with water = $\pi r^{2} h$
                                                            = $9 \pi h$ 
                                            ∵ diameter =18⇒ radius = 9

Volume of 1 sphere = 4/3 π r³
                                  =4/3 π 8
                                  = 32/3 π

Final height rise in beaker = h+40
Final volume = initial volume of cylinder + volume of n spheres
π 9²(h+40) = 81πh+32/3πn
n=  303 .75