Question

a solid iron sphere of diameter 42cm is dropped into a cylinder drum partly filled with water if the radius of drum is 1.4m by how much the surface of water be raised

Answer 1

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