from a circle of radius 15 cm., a sector with angle 216° is cut out and its bounding radii are bent so as to form a cone. Find its volume.
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for this question Lateral surface area(LSA) of cone=area of the sector
=>pi*r1*l=(216/360)*pi*r^2(here l=r=radius of the sector=lateral length of the cone,r1=radius of the cone)
solving it we get,
=>r1=9
now by pythagoras theorem;
r1^2+h^2=l^2
solving it we get
=>h=12
so volume =(1/3)*pi*r1^2*h
so V=(1/3)*pi*9^2*12
solving it we get V=1017.36cu.cm
=>pi*r1*l=(216/360)*pi*r^2(here l=r=radius of the sector=lateral length of the cone,r1=radius of the cone)
solving it we get,
=>r1=9
now by pythagoras theorem;
r1^2+h^2=l^2
solving it we get
=>h=12
so volume =(1/3)*pi*r1^2*h
so V=(1/3)*pi*9^2*12
solving it we get V=1017.36cu.cm
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