Question

AOB is a sector of a circle with radius 6 cm, <AOB =
60°. This sector is bent to form a cone, with AO
touching BO. The base radius of the cone is
A
A
0 1600
B​

Answer 1

Answer:

ANSWER

Since OA=OB, so ΔOAB is an equilateral triangle, therefore, let

∠A=∠B=x

Since the sum of the angles of a triangle is 180

∘

.

x+x+60

∘

=180

∘

2x=180

∘

−60

∘

2x=120

∘

x=60

∘

The area of sector OAB is,

A=πr

2

360

θ

=

7

22

×12×12×

360

60

=75.42cm

2

The area of ΔOAB is,

A=

4

3

(side)

2

=

4

3

×12×12

=62.28cm

2

The difference in the area is,

A=75.42−62.28

A=13.14cm

2

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