Question

A sector containing an angle of 120° is cut off from a circle of radius 21 cm and folded into a cone . Find the curved surface area of the cone.

Answer 1

Step-by-step explanation:

Let r be the base radius of the cone.

Angle of the sector, θ=120

o

Radius of the sector, R=21cm

When the sector is folded into a right circular cone, we have circumference of the base of the cone= Length of the arc

⇒2πr=

360

o

θ

×2πR

⇒r=

360

o

θ

×R

Thus, the base radius of the cone, r=

360

o

120

o

×21=7cm

Also, the slant height of the cone,

l= Radius of the sector

Thus, l=R ⇒ l=21cm

Now, the curved surface area of the cone,

CSA=πrl

=

7

22

×21=462

Thus, the curved surface area of the cone is 462sq.cm