Question

The ratio of the curved surface area to the total surface area of a right circular cylinder is 1:3. Find the volume of the cylinder if its total surface area is 1848cm^2

Answer 1

Curved surface area/Total surface area = 2πr (r + h)/2rh

=>1/3=2πr (r + h)/2πrh
=>r=2h (after calculating)

Total surface area is 1848cm^2
=>2πr (r + h) = 1848cm^2 
=>2π x 2h x(2h+h) = 1848cm^2 (r=2h)
=>h^2=49
=>h=7 (after calculating)

if h=7cm than r = 2x7=14cm

Volume of cylinder = πr^2h=(22/7) x (14)^2 x 7 = 4312cm^3 (ans)

Answer 2

cancelling  we get,
h+r =3 h
r =3h-h
r = 2h.....(1)
tsa of cylinder = 1848

putting value of r we get,


solving this we get,
h = 7
and r = 2*7 = 14
then 
volume of cylinder = 
by subtituting values and further solving it we get volume of cylinder =4312