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Question
A cylindrical jar of radius 6cm contains oil. Iron sphere each of radius 1.5cm are immersed in the oil. How many spheres are necessary to raise level of the oil by two centimetress?
Solution
Given that radius of a cylindrical jar(r) = 6cm
Depth/height of cylindrical jar (h) = 2cm
Let no of balls be ‘n’
Volume of a cylinder = πr2h
V1`=22/7xx(6)^2xx2cm^3` ..........(1)
Radius of sphere 1.5cm
So volume of sphere`=4/3pir^3`
`V^2 = 4/3xx22/7(1.5)^3cm^3` .........(2)
Volume of cylindrical jar is equal to sum of volume of n spheres
Equating (1) and (2)
`22/7xx(6)^2xx2=nxx4/3xx22/4(1.5)^3`
`n=(v_1)/(v_2)`⇒ `n=(22/7xx(6)^2xx2)/(4/3xx22/7(1.5)^3`
n = 16
∴ No of spherical balls (n) = 16
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