A cylindrical vessel 60 cm in diameter is partially filled with water A sphere 30 cm in diameter is ...........

Quantitative Aptitude (CDS) Mensuration 3D

A cylindrical vessel 60 cm in diameter is partially filled with water. A sphere 30 cm in diameter is gently dropped into the vessel and is completely immersed. To what further height will the water in the cylinder rise?

20 cm

15 cm

10 cm

5 cm

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Explanation:

Since the sphere is dropped in the cylindrical vessel partially filled with water and is completely immersed. Therefore, the volumes of both will be equal. Let r be the radius of cylinder and R be the radius of the sphere. Thus, volume of cylinder = volume of sphere
$=>\pi r^{2}h=\frac{4}{3}\pi r^{3}$
$=>30\times30\times h = \frac{4}{3}\times15 \times 15\times 15 \times h[As\: r=30\: and\: R=15]$
=>h = 5
Hence height of water in the cylinder rise = 5 cm