Question

From a circle of radius 15 cm;a sector with angle 216 degrees is cut out and it's bounding radii are bent so as to form a cone.Find it's volume

Answer 1

Answer:

Here,

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

Hence, this is the required result.