State true or false.A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and the height of the cone is 4 cm. The solid is placed in a cylindrical tub full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5cm and its height is 9.8 cm, then the volume of the water left in the tub will be

732.116

cm
3

.

Question

State true or false.A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and the height of the cone is 4 cm. The solid is placed in a cylindrical tub full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5cm and its height is 9.8 cm, then the volume of the water left in the tub will be

732.116 
    
     cm
    3

.

Accepted Answer

Given,The radius of the hemisphere is 2.1 cm and the height of the cone is 4 cm.We have to check if the volume of the water left in the tub will be

732.116 
    
     cm
    3

.Applying the formula for volume of hemisphere: Volume of hemisphere

=
    2
    3
   
   π
    r
    3

∴ Volume of hemisphere =
        2
        3
       
       ×
        
         22
        7
       
       ×2.1×2.1×2.1

⇒ Volume of hemisphere =19.404 
        
         cm
        3

Applying the formula for volume of cone: Volume of cone

=
    1
    3
   
   π
    r
    2
   
   h

∴ Volume of cone =
        1
        3
       
       ×
        
         22
        7
       
       ×2.1×2.1×4

⇒ Volume of cone =18.48 
        
         cm
        3

Thus, volume of object,

=18.48+19.404

=37.884 
        
         cm
        3

Applying the formula for volume of cylindrical tub: Volume of cylinder

=π
    r
    2
   
   h

∴ Volume of cylindrical tub =
        
         22
        7
       
       ×5×5×9.8

⇒ Volume of cylindrical tub =770 
        
         cm
        3

Note that, when the object is immersed in the tub, the volume of water equal to the volume of the object is displaced from the tub.Hence, volume of water left in the tub,

=770−37.884

=732.116 
        
         cm
        3

So, volume of water left in the tub is

732.116 
    
     cm
    3

and thus the statement is true.Therefore, option 1 is correct.

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