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).
Answers
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:
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