The angle of a sector of a circle with radius 42cm is 120 degree if the sector is cut out - Maths - Surface Areas and Volumes

Question

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?

Shruti Tyagi · Accepted Answer

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
Regards

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?