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

An iron pipe 10 cm long has exterior diameter equal to 26 cm. If the thickness of the pipe is 1 cm, Find the whole surface area of the pipe.
A. $frac{21870}{7};cm^{2}$	B. $frac{21780}{7};cm^{2}$	C. $frac{21708}{7};cm^{2}$	D. None of these
Right Option : B
View Explanation

Question : 2

Find the total surface area of the hollowed out cylinder having inner and outer radius 8 cm and 9 cm respectively and height 10 cm.
A. $1174.26;cm^{2}$	B. $1147.36;cm^{2}$	C. $1174.36;cm^{2}$	D. $1174.38;cm^{2}$
Right Option : C
View Explanation

Question : 3

The total surface area of a hollow cylinder which is open from both sides is 4620 sq cm, area of the base ring is 115.5 sq cm and height 7 cm. Find the thickness of the cylinder.
A. $frac{7}{19};cm$	B. $frac{9}{19};cm$	C. $frac{3}{19};cm$	D. none of these
Right Option : A
View Explanation

Chapters

Problems On Boats And Stream

Rules For Divisibility

Square and Square Root

Profit Loss and Discount

Simple and Compound Interest

Ratio and Proportion

Partnership and Mixture

Time, Speed and Distance

Quadratic Equations

Time and Work

Mensuration

Surface Area and Volume

Introduction to Trigonometry

Permutation and Combination

Content / Category

IMO-Mathematics Olympiad

Central Government Service

ISO - Science Olympiads

State Government Services

Banking And Insurance

Railways & Metro Services

MBA Entrance

Law Entrance

English Proficiency

Reasoning Proficiency

Computer Proficiency

Navodaya Entrance 6th & 9th

Sainik School Entrance

Andhra Bank

Class / Course

General Awareness For SSC

SSC CHSL

General Knowledge For SSC

SSC MTS

SSC CHSL Test Series

SSC CGL

Students / Parents Reviews [20]

My experience with Abhyas Academy has been very good. When I was not in Abhyas whenever teacher ask questions I could not speak it confidently but when I came in Abhyas, my speaking skills develope...

Upmanyu Sharma

7th

It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.

Cheshta

10th

My experience with Abhyas academy is very nice or it can be said wonderful. I have been studying here from seven class. I have been completing my journey of three years. I am tinking that I should ...

Hridey Preet

9th

Being a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from m...

Prisha Gupta

8th

One of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develo...

Aman Kumar Shrivastava

10th

In terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to asses...

Aman Kumar Shrivastava

10th

Third consective year,my ward is in Abhyas with nice experience of admin and transport support.Educational standard of the institute recumbent at satisfactory level. One thing would live to bring in notice that last year study books was distributed after half of the session was over,though study ...

Ayan Ghosh

8th

Abhyas academy is great place to learn. I have learnt a lot here they have finished my fear of not answering.It has created a habit of self studying in me.The teachers here are very supportive and helpful. Earlier my maths and science was good but now it has been much better than before.

Barkha Arora

10th

Abhyas is good institution and a innovative institute also. It is a good platform of beginners.Due to Abhyas,he has got knoweledge about reasoning and confidence.My son has improved his vocabulary ...

Manish Kumar

10th

I have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying

Yatharthi Sharma

10th

My experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.

Hiya Gupta

8th

Abhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.

Manish Kumar

10th

It has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice

Barkha Arora

10th

Abhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.

Om Umang

10th

Abhyas is an institute of high repute. Yogansh has taken admission last year. It creates abilities in child to prepare for competitive exams. Students are motivated by living prizes on basis of per...

Yogansh Nyasi

7th

Abhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...

Aman Kumar Shrivastava

10th

My experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.

Ayan Ghosh

8th

Abhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are v...

Abhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are very helpful in solving the problems. The major advantages of the institute is extra classes for weak...

Shreya Shrivastava

8th

The experience was nice. I studied here for three years and saw a tremendous change in myself. I started liking subjects like English and SST which earlier I ran from. Extra knowledge gave me confi...

Aman Kumar Shrivastava

10th

It was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.

Eshan Arora

8th

View All

Attention !!!!!