Question

From each end of a metal cylinder, metallic hemispheres were scooped out. The height of cylinder is 10cm and radius is 4.2 cm. The rest of the cylinder is converted to a wire if thickness 1.4cm. Find the length of wire

Answer 1

Given Height of cylinder  =  10 cm
And
Radius  =  4.2 cm
And , as given,  From each end of a solid metal cylinder,metal was scooped out in hemispherical form of same diameter. So
Radius of hemisphere  =  4.2 cm
And
Volume of cylinder after scooped out in hemispherical form  =  Volume of cylinder -  2 (  Volume of hemispherical form scoop )

We know  Volume of cylinder =

π 

r

2

 h


So,
Volume of a cylinder =

22

7

× 4.2× 4.2 ×10= 22× 0.6× 4.2 ×10

  =  554.40  c

m

3

 

 


And
We know Volume of hemisphere  = 

2 π 

r

3

3

 
So,
Volume of hemisphere scoop  = 

2 ×

22

7

× 4.2× 4.2× 4.2

3

 = 2 × 22 × 0.6× 1.4×

 4.2 = 155.232 c

m

3

 
So,
Volume of cylinder after scooped out in hemispherical form  = 554 . 40 -  2 ( 155.232 )  = 554 . 40 - 310.464 =  243.936 cm3
And
As given : The rest of the cylinder is melted and converted into a cylindrical wire of thickness 1.4cm.  , So
Diameter of cylindrical wire  =  1.4 cm  , So radius of wire  = 0.7 cm 
And
Let length ( Height )  of wire  =  h  
And
Volume of wire  =  Volume of cylinder after scooped out in hemispherical form 
So,

π 

r

2

 h =  243.936

⇒

22

7

× 0.7× 0.7× h = 243.936

⇒22× 0.1× 0.7× h = 243.936

⇒ 1.54 h = 243.936

⇒ h = 158.4


So,
Length  of wire  =  158.4  cm                                           

Answer 2

Answer:

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