Question

A sphere of radius 6 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 8 cm. If the sphere is submerged completely, then the surface of the water rises by
(a)4.5 cm
(b)3
(c)4 cm
(d)2 cm

Answer 1

Answer:

The surface of the water rises by = 4.5 cm  .

Among the given options option (a) 4.5 cm is  the correct answer.

Step-by-step explanation:

Given :  

Radius of the sphere ,r =  6 cm

Radius of the cylindrical vessel, R = 8 cm

Let the level of water rises = h cm

Sphere is dropped into the cylindrical vessel then their volumes are equal.

Volume of the water raised in the cylindrical vessel = Volume of the sphere

πR²h = 4/3 × πr³

R²h = 4/3 ×r³

8² × h = 4/3 × 6³

64 × h = 4/3 × 216

64 × h = 4× 72

h = (4 × 72)/64

h = 4 × 9/8

h = 9/2  

h = 4.5 cm

Surface of the water rises by = 4.5 cm  

Hence, the surface of the water rises by = 4.5 cm  

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Answer 2

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