SURFACE AREAS

AND VOLUMES

• Cone-Introduction

• Sum based on Cone

Examples :

Ice Cream cone

Conical candles

Sand cone

Let us see some examples of Right Circular Cone

r

h

l

1

2

• A Right Circular Cone has two faces.

• One circular face

1

• One curved face

• A cone has radius (r),

height (h) and

slant height (l )

Let us see geometrical figure of right circular cone

R

L

r

h

l

Now, we understand that,

Area of sector = CSA of cone

Area of sector

=

CSA of cone

L × R

2

=

CSA of cone

2πr ×

l

2

=

CSA of cone

CSA of cone

=

π rl

CURVED SURFACE AREA CONE

Observe a sector whose,

Radius

=

R

length of arc

=

L

Let us fold the sector

to form an open cone.

Radius of the cone = r

Height of the cone = h

Slant height of the cone = l

Now, length of arc =

Circumference

2πr

Radius of sector =

Slant height of cone

TSA =

CSA +

Area of circular face

=

πrl

Area of circular face = πr²

πr²

+

=

πr

( l + r )

Total surface area =

π r ( r + l )

Volume

1

3

×

πr²h

=

Diameter (d) = 70 cm

​

∴ Radius (r) =

​

Curved surface area of cone = rl

Sol.

∴ 4070 =

× 35

× l

4070 × 7

22 × 35

= l

l = 37 cm

∴ Slant height of a cone is 37 cm.

70

2

= 35 cm

∴

5

814

37

35

Q. The curved surface area of a cone is 4070 cm² and its diameter is 70 cm.

What is its slant height ?

Curved surface area of a cone = 4070cm²

What is formula for curved surface area of cone?

πrl

To find : l