Radius of the circle = R=5cm, angle of the sector = θ=216°.
Length of the circular arc cut off from the circle
L=2πR×360°θ=2π(5)360°216°=6π(cm) When the sector is cut and its bounding radii is bent to form a cone, slant height of the cone, l=R=5cm.
Let r and h be the radius and height of the cone formed.
Circumference of the base of the cone =2πr=6π.
r=3cm.The base radius is 3cm.
Height of the cone
h=l2−r2=52−32=4(cm) Let φ be a vertical angle. Then
sin(φ/2)=lr=53=0.6
φ=2arcsin(0.6)≈73.74° Find the curved surface area
πrl=π(3)(5)=15π(cm2)≈47.12(cm2)
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