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)`

Explanation

Total surface area of the cylinder `(TSA)=462 cm^2`
Curved surface of the cylinder `(CSA)=13xxTSA`
`=13xx462`
`=154cm^2`
Area of each circle`=(TSA−CSA)/2`
`=(462−154)/2` [`∵ TSA = CSA + 2` circular base area]
`=154cm^2`
`∴pixxr^2=154` [`∵` Area of the circle`=pir^2`]
`⇒r^2=49`
`⇒r=7`
And,
`2pirh=154` [`∵`curved surface of the cylinder`=2pirh`]
`2xx22/7xx7xxh=154`
`⇒h=154/44`
`⇒h=3.5cm`
Hence, the volume of the cylinder is `3.5cm`.