Question

a solid cylinder has a total surface area of 231 cm square ,its curved surface area is 2/3 of its total surface area.find the volume of the cylinder.

Answer 1

t.s.a of cylinder = 2πr(r+h)= 231 cm^2
2π(r^2+rh)=231
r^2+rh = 231*7/44
36.75=r(r+h)
r+h= 36.75/r
h= (36.75/r)-r.................(1)
c.s.a of cylinder = 2πrh=2/3*231=154
44rh/7=154
rh = 154*7/44=24.5
h= 24.5/r.....................(2)

From (1)&(2)
h=(36.75/r)-r = 24.5/r
36.75-r^2/r= 24.5/r
36.75-r^2 = 24.5
-r^2= 24.5 -36.75=-12.25
r^2 = 12.25
r = 3.5 cm
from (2)
h = 24.5/r= 24.5/3.5 =7 cm


Now, volume of cylinder =πr^2h = 22/7*(3.5)^2*7
= 22*12.25
= 269.5 cm^3
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Answer 2

CSA = 2πrh
154 = 2πrh
so, rh = 49/2
now, TSA = 2πr(r+h)
231 = 2πr² +2πrh
so, r= 7/2 cm and h = 2 cm
now , volume = 77 cm³