Surface Area of Hollow Cylinder


 
 
Concept Explanation
 

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

(iii) Total Surface Area =2pi Rh+2pi rh+2pi (R^{2}-r^{2})

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

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

Illustration: Find the total surface area of the hollowed out cylinder shown in the adjacent figure.

Solution: Total surface area of hollow cylinder = Outer CSA + Inner CSA + top and bottom ringed area

                                                                   =2pi r_{1}h+2pi r_{2}h+2pi (r_{1}^{2}-r_{2}^{2})

                                                                   =2pi [5times 18+4times 18+(5^{2}-4^{2})];cm^{2}

                                                                  =2pi(90+72+9);cm^{2}

                                                                  =342times 3.14;cm^{2}

                                                                 =1073.88;cm^{2}

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

(iii) total 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}

(iii) Total surface Area = Inner Curved surface Area + outer curved surface Area + top and bottom ringed area

                               =968;cm^{2}+1064.8;cm^{2}+2pi (r_{1}^{2}-r_{2}^{2})

                              =2032.8;cm^{2}+2times frac{22}{7}times left ( 4.84-4 right );cm^{2}

                              =(2032.8+5.28);cm^{2}

                              =2038.08;cm^{2}                         

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

Find the total surface area of the hollowed out cylinder having inner and outer radius 1 cm and 2 cm respectively and height 4 cm.

Right Option : D
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Explanation
Question : 2

Find the total surface area of the hollowed out cylinder having inner and outer radius 2 cm and 3 cm respectively and height 5 cm.

Right Option : A
View Explanation
Explanation
Question : 3

Find the total surface area of the hollowed out cylinder having inner and outer radius 3 cm and 5 cm respectively and height 7 cm.

Right Option : B
View Explanation
Explanation
 
 
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