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?

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#### 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 = πr^{2}h

V_{1}`=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

Concept: Volume of a Combination of Solids

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