A sector of a circle of radius 10 cm is folded such that it forms into a cone. If the central angle of the sector is 144∘ then what is the volume of the cone formed ? (in cm3 )
704√2121
628√1111
576√2121
682√1111
A
628√1111
B
704√2121
C
576√2121
D
682√1111
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Solution
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Slant height of cone = radius of circle from which sector is cut
l=10cm
Area length of 1440 sector =2π×radius×14403600
=2π×10×144360=8π
Circumference of the base of cone = arc length =8π cm
∴2πr=8π⇒r=4cm
h=√l2−r2=√102−42=√100−16=√84=2√21
∴ Volume of cone =13πr2h=13×227×4×4×2√21
=704√2121
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