The ratio between the curved surface area and the . . .

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

Doubt by Saksham

Solution : 

CSA of Cylinder : TSA of cylinder = 1:2 (Given)

2πrh/2πr(h+r) = 1/2
h/(h+r) = 1/2
2h = h+r
2h-h=r

h=r

TSA of cylinder = 616 cm²

2πr(h+r) = 616

2πr(r+r) = 616 [∵ h=r]

2πr(2r) = 616

4πr² = 616

πr² = 616/4

(22/7)r² = 154
r² = (154×7)/22
r² = 7×7
r =√(7×7)
r = 7 cm 

Volume of Cylinder 

= πr²h

= (22/7)×(7)²×7
= 22×49
= 1078 cm³

Hence, the volume of the cylinder is 1078 cm³