A hollow right circular culinderical vessel of volume V whose diameter is equal to its height is com...........

Quantitative Aptitude (CDS) Mensuration 3D

A hollow right circular culinderical vessel of volume V whose diameter is equal to its height, is completely filled with water. A heavy sphere of maximum possible volume is then completely immersed in the vessel . What volume of water remains in the vessel?

V/2

V/3

2V/3

V/4

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Explanation:

As per the given condition , the radius of sphere and cylinder will be same.
V= $\pi$ r²h= $\pi$ r²D=2 $\pi$ R³
V_s=4/3 $\pi$ R³
V_{s /} V = (4/3 $\pi$ R³)/2 $\pi$ R³ = 2/3
V_s=2V/3