Question

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

Answer 1

Answer Radius of the circle =r=15 cm. angle of the sector =θ=216°. Length of the circular arc cut off from the circle = 360° 2πr×θ = 360°×7 2×22×15×216 ∘ = 7 396 cm As the piece is bent into a right circular cone. So, the slanting height h of the cone =radius of circle=R=15cm. h=15 cm circumference of the base of the cone = arc length = 7 396 cm Base radius R of the cone =R= 7 396 × 2π 1 =9 cm Height of the cone =H= (h 2 −R 2 ) = (15 2 −9 2 ) =12 cm Volume of the cone =V= 3 1 π×R 2 H V= 7 22 × 3 1 ×9 2 ×12cm 3 V= 7 7128 cm 3 V=1018.29 cm 3 .

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

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