Question

From a circle of radius 15cm a sector with angle 216 degree is cut out and its bounding radii are bent so as to form a cone find the volume

Answer 1

Radius of the circle = R = 15 cm.
angle of the sector = Ф = 216°.

Length of the circular arc cut off from the circle 
   = 2 π R * Ф/360°
   = 2 * 22/7 * 15 * 216/360  cm
  =  396/7 cm

The piece is bent into a right circular cone.
So the slanting height s of the cone = radius of circle = R = 15 cm.
s = 15 cm
circumference of the base of the cone = arc length = 396/7 cm
base radius r of the cone = r = 396 /7 * 1/2π = 9 cm
height of the cone = h = √(s² - r²) = 15² - 9²) = 12 cm 

Volume of the cone = V = π/3 * r² h 
 V = 22/7 * 1/3 * 9² * 12 cm³
    = 7128/7 cm³

Answer 2

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