The angle of a sector of a circle with radius 42cm is 120 degree.if the sector is cut out and used to make a cone,what is the curved surface area, total surface area and volume of the cone?  

Dear student,

The length of the arc of the sector is the circumference of the base of the cone.θ360×2πR=120°360°×2π×42=π3×42×2=28πcircmuference of base of cone=2πr=28πr=14cmfor a cone we have r=14 cm, side length of cone l=42cm so, h=l2-r2=422-142=1568=39.5cmCurved surface area of cone=πrl=227×42×14=1848 cm2Total Surface area of cone=πrl+πr2=πr(l+r)=227×1442+14=22×2×56=2464 cm2Volume of cone=13πr2h=13×227×14×14×39.5=8110.66 cm3
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Danteshwar here is your answer.

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