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.
A. $49.2;cm^{2}$	B. $44.2;cm^{2}$	C. $75.2;cm^{2}$	D. $94.2;cm^{2}$
Right Option : D
View Explanation

Question : 2

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 : 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.
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

Chapters

Square and Square Root

Cube and Cube Roots

Time, Speed and Distance

Partnership and Mixture

Permutation and Combination

Introduction to Trigonometry

HCF And LCM

Number Theory

Rules For Divisibility

Problems On Boats And Stream

Mensuration

Profit Loss and Discount

Simple and Compound Interest

Surface Area and Volume

Content / Category

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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

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