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.
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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
Now, height of the cone can be calculated as,
➣ h² = l² - r²
➣ h² = (15)² −( 9)²
➣ h² = 225 − 81
➣ h = = 12 cm
Therefore,
Volume of the cone, V = 3/1 πr² h= 3/1 × 22/7 ×81×12 = 1018.28 cm³
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- Hence, this is the required result.
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