a solid cylinder has total surface are of 462 cm2 and its lateral surface area is one-third of its total surface area . find the volume of the cylinder.
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l.s.a.=t.s.a./3
2#rh=(2#rh+#r^2)/3
2#rh=2#r (h+r)/3
h=(h+r)/3
so h =r/2
now
t.s.a=462
2#rh+2#r^2=462
2#r (h+r)=462
2#r (r/2+r)462
r=7 cm
h=7/2
volume= #r^2h
=(22*7*7*7)/7*2
=539
2#rh=(2#rh+#r^2)/3
2#rh=2#r (h+r)/3
h=(h+r)/3
so h =r/2
now
t.s.a=462
2#rh+2#r^2=462
2#r (h+r)=462
2#r (r/2+r)462
r=7 cm
h=7/2
volume= #r^2h
=(22*7*7*7)/7*2
=539
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