Question

A sector of central angle 120° and a radius of 21
cm were made into a cone. Find the height of the
cone (in cm).​

Answer 1

Step-by-step explanation:

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

Answer 2

Answer:

Hello...

Given, a sector of a circle of radius 6 cm has an angle of 120 degrees.

Now, it is rolled up so that the two bounding radii are joined together to form a cone.

So, circumference of the base of cone = Length of the arc of the sector

= (θ/360) * 2πr

= (120/360) * 2π * 6

= (1/3) * 2π * 6

= 4π

We know that circumference of circle = 2πr

So, circumference of base of cone = 2πr

=> 2πr = 4π

=> r = 2

So, the radius of base of cone r = 2 cm

Slant height of the cone l = radius of the sector = 6 cm

We know that slant height l = √(h2 + r2 )

6 = √(h2 + 22 )

=> 62 = h2 + 4

=> 36 = h2 + 4

=> h2 = 36 - 4

=> h2 = 32

=> h = √32

=> h = 4√2

=> h = 4 * 1.414

=> h = 5.656

=> h ≈ 5.66

So, the height of the cone h = 5.66 cm

1. Volume of cone = (1/3) * πr2 h

= (1/3) * (22/7) * 22 * 5.66

= (1/3) * (22/7) * 4 * 5.66

...... hope it will help you ✌✌