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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 cm2, then its volume is ?
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- 1632 cm3
- 1078 cm3
- 1232 cm3
- 1848 cm3
Correct Option: B
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
