State true or false.Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height are 7 cm. Check whether the cylinder with greater volume also has greater surface area.

Question

Accepted Answer

It is given that the diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm and a figure,

Surface area of a cylinder =2πr(r+h)
  . Radius of cylinder.Volume of a cylinder

=π
    r
    2
   
   h
  .Volume of the cylinder A is;

⇒π×
      r
      2
     
     ×h

⇒
      
       22
      7
     
     ×

7
         2

2
     
     ×14

⇒
      
       22
      7
     
     ×
      7
      2
     
     ×
      7
      2
     
     ×14

⇒22×
      7
      2
     
     ×
      7
      2
     
     ×2

⇒11×7×7×1

⇒539
      cm
      3

Diameter of the cylinder B = 14 cm.Radius of the cylinder

B=
    
     14
    2
   
   cm=7cm
  Height of the cylinder B = 7 cm. Volume of a cylinder

=π
    r
    2
   
   h
  .Volume of the cylinder B is;

⇒π×
      r
      2
     
     ×h

⇒
      
       22
      7
     
     ×
      7
      2
     
     ×7

⇒
      
       22
      7
     
     ×7×7×7

⇒22×7×7×1

⇒1078
      cm
      3

Surface area of the cylinder A is;

⇒2πr(r+h)

⇒2×
      
       22
      7
     
     ×
      7
      2
     
     ×

7
        2
       
       +14

⇒22×

7
        2
       
       +14

⇒385
      cm
      2

Surface area of the cylinder B is;

⇒2πr(r+h)

⇒2×
    
     22
    7
   
   ×7×(7+7)

⇒2×22×14

⇒616
    
     cm
    2

It can be concluded that a cylinder with greater volume also has greater surface area.Cylinder

B
  has greater volume as well as greater surface area than cylinder

A
  .Given statement is true.Hence option (1) is correct.

State true or false.

Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height are 7 cm. Check whether the cylinder with greater volume also has greater surface area.

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