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 2 cm, 3 cm respectively and height is 6 cm.
A. $frac{1320}{7}; cm^{2}$	B. $frac{1302}{7}; cm^{2}$	C. $frac{1300}{7}; cm^{2}$	D. $frac{1322}{7}; cm^{2}$
Right Option : A
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Question : 2

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.
A. $frac{1544}{7}; cm^{2}$	B. $frac{1588}{7}; cm^{2}$	C. $frac{1548}{7}; cm^{2}$	D. $frac{1584}{7}; cm^{2}$
Right Option : D
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Question : 3

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.
A. $71.9; cm^{2}$	B. $72.7; cm^{2}$	C. $72.9; cm^{2}$	D. $79.2; cm^{2}$
Right Option : D
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