If a cylinder is having ratio of curved surface area to its total surface area as 1:2 and its total surface area as

616 c
m
2

,
its volume will be ____

cm
3

.

Question

If a cylinder is having ratio of curved surface area to its total surface area as 1:2 and its total surface area as

616 c
    m
    2
   
   ,
   its volume will be ____

cm
    3
   
   .

Accepted Answer

If a cylinder is having ratio of curved surface area to its total surface area as 1:2 and its total surface area as

616 c
    m
    2
   
   ,
   its volume will be

1078 
    
     cm
    3
   
   .
  It is given that a cylinder is having ratio of curved surface area to its total surface area as 1:2 and its total surface area as

616 c
    m
    2
   
   .
  We know thatCurved surface area of a cylinder =

2πrh.
   Total surface area of the cylinder =

2πr
    
     h+r
   .
   Volume of the cylinder =

π
    r
    2
   
   h,
   where r is the radius of the cylinder and h is the height of the cylinder.Given that the ratio of C.S.A to T.S.A is 1 : 2. So, we can have,

2πrh
      
       2πr
        
         h+r

=
      1
      2

⇒
      h
      
       h+r
     
     =
      1
      2

⇒h+r=2h

⇒h=r

We have got a relation between height and the radius.Since the total surface area of a cylinder is

616 
    
     cm
    2
   
   ,
   we can calculate height of the cylinder as,

616=2πr
      
       r+r
          
      
       ∵h=r

⇒616=2πr×2r

⇒616=4π
      r
      2

⇒
      r
      2
     
     =
      
       616×7
      
       4×22

⇒r=7

⇒h=7     
      
       ∵h=r

Finally, we can calculate the volume of the cylinder as shown,

V=π
      r
      2
     
     h

=
      
       22
      7
     
     ×7×7×7

=1078 
      cm
      3

Therefore, the volume of the cylinder is

1078 
    
     cm
    3
   
   .

If a cylinder is having ratio of curved surface area to its total surface area as 1:2 and its total surface area as $616 c m 2,$ its volume will be ____ $cm 3 .$

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If a cylinder is having ratio of curved surface area to its total surface area as 1:2 and its total surface area as 616 c m 2 , its volume will be ____ cm 3 .