Question

A solid iron sphere of diameter 42 cm is dropped into a cylindrical drum partly
filled with water. If the radius of the drum is 1.4 m. by how much will the surface
of the water be raised?​

Answer 1

Answer:

Let r & R be the radius of the sphere and cylindrical vessel respectively.

Now,  2r=18cm⇒r=9cm

       2R=36cm⇒R=18cm

Let the rise in water level in the cylindrical vessel be  

′

h  

′

cm.

Volume of sphere =  

3

4

​  

πr  

3

 

Volume of liquid displaced in the cylindrical vessel =πR  

2

h

If the sphere is completely submerged in the vessel, then volume of liquid displace in the cylindrical vessel = Volume of the sphere

∴πR  

2

h=  

3

4

​  

πr  

3

⇒(18)  

2

×h=  

3

4

​  

×(9)  

3

 

⇒h=  

3×(18)  

2

 

4×(9)  

3

 

​  

=3cm

Thus, the rise in water level in the cylindrical vessel is 3cm

Answer 2

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