SURFACE AREAS

AND VOLUMES

• CYLINDER - Introduction

Examples :

Roller wheels

Pipes

Cylindrical candles

Let us see few examples

of right circular cylinder

​

• Cylinder has radius ‘r’ and height ‘h’.

• The right circular cylinder has three faces.

Let us see geometrical figure

of right circular cylinder

​

3

1

2

• Two circular faces

• One curved face

A cylinder has two circular

faces of same radii

h

r

1

r

Distance between the centers

of the circular faces is the

height of the cylinder

Height is the

perpendicular distance

Let us take a

rectangular-sheet of

length l and breadth b

b

l

Area of this sheet = l × b

Let us fold the

sheet to form an

open cylinder

Now, we understand that,

Let the radius of the

cylinder be ‘r’ and

height be ‘h’

Let us first understand

formula for curved

surface area of cylinder

Area of the sheet =

l

×

b

CSA of cylinder =

Area of sheet =

CSA of cylinder

CSA of cylinder

=

CSA of cylinder

When we fold the sheet lengthwise,

length of sheet =

Circumference

2πr

2πr ×

Breadth of sheet =

h

h

=

CSA of cylinder

2πrh

2 π r (r + h)

Total Surface Area =

TSA =

=

+

CSA of a cylinder

Area of 2 circular faces

2πrh

Area of a circular face

+

×

2

The circular faces have

equal radii and are

parallel to each other

Area of circular face = πr²

2 π r

=

(h + r)

2πrh

+

πr²

=

2

Volume

=

Volume of cylinder =

Area of base

=

× Height

×

Volume of the cylinder is

the capacity of the cylinder

The circular faces of the

cylinder have equal radii

and are parallel to each other

Area of circular face = πr²

πr²

h

πr²h