State true or false.A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Its surface area will be

220

mm
2

.

Question

State true or false.A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Its surface area will be

220 
    
     mm
    2

.

Accepted Answer

Given,The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm.We have to check if the surface area will be

220 
    
     mm
    2

.Using the formula,

(r)=
    
      diameter 
    2

Constructing the required diagram:

∴r=
    5
    2
   
    mm
   Understand that, the height of the cylinder:

∴h=14−
        
         2×
          5
          2

⇒h=9 mm

Note that, Curved surface area of cylinder

=2πrh
   Curved surface area of hemisphere

=2π
    r
    2

Total surface area of the capsule = Curved surface area of cylinder

+2x
   curved surface area of a hemisphere.

∴ Total surface area of the capsule =2πrh+2×2π
      r
      2

⇒ Total surface area of the capsule

=2πr(h+2r)

=2×
          
           22
          7
         
         ×
          5
          2
         
         ×
          
           9+2×
            5
            2

=
          
           22
          7
         
         ×5×(9+5)

Simplifying further,

⇒ Total surface area of the capsule

=
        
         22
        7
       
       ×5×14

=220 
        
         mm
        2

So, the surface area of the medicine capsule is

220 
    
     mm
    2

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

State true or false.

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Its surface area will be $220 mm 2$ .

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State true or false.A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Its surface area will be 220 mm 2 .

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State true or false.

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Its surface area will be $220 mm 2$ .