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 3 cm and 5 cm respectively and height 7 cm.
A. $422.26;cm^{2}$	B. $452.16;cm^{2}$	C. $452.26;cm^{2}$	D. $451.26;cm^{2}$
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

HCS Prelims

SETC Exam Preparation

Haryana GK

HCS Prelims Test Series

Students / Parents Reviews [10]

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

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

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

A marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre f...

Archit Segal

7th

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

My experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak poi...

Shivam Rana

7th

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

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 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

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

View All

Attention !!!!!