The curved surface area and the total surface area of a cylinder are in the ratio 1 : 2. If the total surface area of the right cylinder is 616 cm 2, then its volume is?

Curved surface area of cylinder = 2πrh cm²
Total surface area of cylinder = 2πr(h + r) cm²
Now, According to the question
2πrh/2πr(h + r) = 1/2
⇒ h/(h + r) = 1/2
⇒ 2h = h + r
∴ Now, Total surface area = 616 cm²
⇒ 2π (h + r) = 616
⇒ 2πr (r + r) = 616 (∵ h = r)
⇒ 2πr(2r) = 616
⇒ 4πr² = 616
⇒ r = √style="text-decoration:overline">616/4π
= √616 x 7/4 x 22
= √7 x 7 =
∴ r = h = 7 cm
∴ Volume = π r² h
= (22/7) x (7 x 7) x 7 = 1078 cm³