Question

from a circle of radius 15cm., a sector with angle 216 degrees is cut out and it's 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 = 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

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