A solid cylinder has total surface area of 462 square cm. Its curved surface area is one-third of its total surface area. Find the volume of the cylinder. (Take `pi=22//7)`

Answer

`539 cm^(3)`

Explanation

Curved surface area `= ((1)/(3) xx 462) cm^(2) = 154 cm^(2)`
`2pi rh = 154 ...(i) " " and 2pir (h + r) = 462`...(ii)
`:. (2pirh)/(2pir(h + r)) = (154)/(462) = (1)/(3) rArr (h)/(h + r) = (1)/(3)`
`rArr 3h = h + r rArr r = 2h`
Putting r = 2h in (i), we get `h^(2) = (49)/(4) = ((7)/(2))^(2) rArr h = (7)/(2)`
Thus, r = 7 and h = 3.5. Now, find the volume