Question

What is the height of a cone made by rolling a sector of radius 12 cm and central angle 120

Answer 1

Step-by-step explanation:

Given the radius of circle 12cm

This becomes the slant height of cone

The angle of sector 120

∘

The length of arc is given as=

360

x

×2πr

360

120

×2×π×12

3

1

2π×12

2π×4

8π

This become the circumference of base circle= 2πr=8π

2r=8

r=4

According to Pytagorous theorm

(Slantheight)

2

=(height)

2

+(radius)

2

12

2

=(height)

2

+4

2

144=(height)

2

+16

(height)

2

=144−16

(height)

2

=132

height=

132

Volume of cone=

3

1

πr

2

h

3

1

×

7

22

×4×4×

132

21

362

132