Question

From a circle of radius 15 cm., a sector with angle 216° is cut out and its bounding radi
are bent so as to form a cone. Find its volume.​

Answer 1

Answer:

Radius of the circle, R=15 cm

 

When the sector is cut and its bounding radii is bent to form a cone,

Slant height of the cone, l=R=15 cm

 

Let r and h be the radius and height of the cone, respectively.

 

Again, we know that in a circle of radius R, an arc of length X subtends an angle of θ radians, then

x=Rθ

 

Here, the arc length will be equal to the perimeter of the base circle of the cone.

x=2πr

2πr=Rθ

R

r

​  

=  

2π

θ

​  

 

⇒  

15

r

​  

=  

360

216

​  

 

⇒r=9 cm

 

Now, height of the cone can be calculated as,

h  

2

=l  

2

−r  

2

 

h  

2

=(15)  

2

−(9)  

2

 

h  

2

=225−81

h=  

144

​  

=12 cm

 

Therefore,

Volume of the cone, V=  

3

1

​  

πr  

2

h=  

3

1

​  

×  

7

22

​  

×81×12=1018.28 cm  

3

Step-by-step explanation:

i hope it helps