Question

A metal sphere of diameter 42 centimetre immersed into a cylindrical drum partly filled with water if the diameter of the drum is 140 CM by much will the surface of the water in the drum be raised​

Answer 1

Answer:

Step-by-step explanation:

Step-by-step explanation:

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

diameter of sphere(d)= 42 cm

radius= 42/2=21cm

diameter of cylindrical drum=140cm

radius=140/2=70cm

As, the metal sphere is immersed into a cylindrical

drum,

Vol. of sphere=Vol.of cylindrical drum

or, 4/3*pi*r^3=pi*r^2*h [cancelling pi from both sides]

or, 4/3*(21)^3=(70)^2*h

or, 12348=4900*h

or, h=12348/4900

therefore, h=2.52 cm

Water in drum will be raised by 2.52 cm

I bet this is the correct answer

hope this helps

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