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msingh
A cylinder of diameter 10cm and a height of 20 cm is filled with water . if a sphere of diameter 10 cm is completely submerged inside the cylinder ,what will be the increase in the level of water, in the cylinder?
1) Find volume of the sphere 2) Equate the volume of sphere with formula of volume of cylinder to find increase in height
V of sphere= (4/3) r^3 =(4/3) 5^3 =500/3
V of cyl=pi r^2h =pi(5^2) (20) =500pi
Volume of cylinder = pir^2 h = 500pi volume of sphere immersed = 4/3pi r^3 = 500pi/3 New volume of cylinder = Initial cylinder volume + Sphere volume. pi*25*h = 500pi +500pi/3 h = 20(4/3) =80/3 hence change in height = h-20 = 20/3