Question

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.

Answer 1

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

Answer 2

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