Lateral Surface Area of Hollow Cylinder


 
 
Concept Explanation
 

Lateral Surface Area of Hollow Cylinder

Hollow Cylinder: A solid bounded by two co-axial cylinders of the same height and different radii is called a hollow cylinder. Solids like iron pipes, rubber tubes etc. are hollow cylinder.

Let R and r be the external and internal radii of a hollow cylinder and h be its height as shown in the following figure.

Then we have the following results:

(i) Each base Surface Area = pi (R^{2}-r^{2});sq;units

(ii) Curved(Lateral) surface Area = (External surface area) + (Internal surface Area)

                                              =2pi Rh+2pi rh

                                              =2pi h(R+r);sq; units

Illustration: An iron pipe 20 cm long has exterior diameter equal to 25 cm. If the thickness of the pipe is 1 cm, Find the whole surface area of the pipe.

Solution: We have,

R = External radius = 12.5 cm

r = Internal radius   = (External radius - Thickness)

 = 12.5 - 1    = 11.5 cm

h = length of the pipe = 20 cm

So, Total Surface Area of the Pipe =  (External curved surface) + (Internal curved surface) + 2(Area of the base of the ring)

                                                  =2pi Rh +2pi rh+2(pi R^{2}-pi r^{2})

                                                 =2pi(R+r)h +2pi (R^{2}-r^{2})

                                                =2pi(R+r)h +2pi (R-r)(R+r)

                                              =2pi(R+r) (h+R-r)

                                             =2times frac{22}{7}times (12.5+11.5)times (20+12.5-11.5);cm^{2}

                                          =2times frac{22}{7}times (24)times (21);cm^{2}

                                           =3168;cm^{2}

Illustration: A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm. Find its

  • (i) inner curved surface area
  • (ii) outer curved surface area
  • Solution: Length of the metal pipe = 77 cm(h)

    Inner radius (r_{2})=frac{4}{2}=2;cm

    Outer radius (r_{1})=frac{4.4}{2}=2.2;cm

    (i) Inner Curved Surface Area =2pi r_{2}h

                                            =2times frac{22}{7}times 2times 77

                                            =968;cm^{2}

    (ii) Outer Curved Surface Area =2pi r_{1}h

                                               =2times frac{22}{7}times 2.2times 77

                                             =1064.8;cm^{2}

                                

    Illustration: Find the outer and inner curved surface area of the hollowed out cylinder shown in the adjacent figure.

    Solution:   Height of the cylindrical pipe is 77 cm.  Inner diameter = 4 cm. So, inner radius = 2 cm.   Outer diameter = 4.4 cm. So, outer radius = 2.2 cm

                 

    Sample Questions
    (More Questions for each concept available in Login)
    Question : 1

    Find the lateral surface area of the hollow cylinder if inner and outer radii are 4 cm, 7 cm respectively and height is 7.7 cm.

    Right Option : C
    View Explanation
    Explanation
    Question : 2

    Find the lateral surface area of the hollow cylinder if inner and outer radii are 2 cm, 3 cm respectively and height is 2.1 cm.

    Right Option : D
    View Explanation
    Explanation
    Question : 3

    Find the lateral surface area of the hollow cylinder if inner and outer radii are 2 cm, 4 cm respectively and height is 6 cm.

    Right Option : D
    View Explanation
    Explanation
     
     
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