# The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2.

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The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the volume of the cylinder, if its total surface area is 616 cm2.

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Given,

and, total surface area of cylinder = 616 cm2

= h = r

So, 2πr(h + r) = 616

= 2πr(2r) = 616

= 49

= r = $\sqrt{49}$ = 7 cm

Hence, volume of cylinder = πr2h

$\cfrac{22}7\times$49$\times$7 = 1078 cm3

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CSA= 2πrh
TSA= 2(πrh+πr2)
CSA/TSA=1/2
by simplifying we'll get h=r......(1)
now 2(πrh+πr2)= 616
put h=r from 1
we'll get
2(πr2+πr2)=616
solving it will give
r=7
and V=πr2h
putting values will give us
V=1078 cm3