A solid cylinder has a total surface area of `231 cm^2dot` Its curved surface area is `2/3` of the total surface area. Find the volume of the cylinder.

Explanation

Given total surface Area =`231 cm^2`
and curved surface area =`3//2xx231`
=`2xx77`=`154 cm^2`
We know that `2pir(h+r)=231`
And `2pirh` =`154`
Therefore,`2pirh+2pir^2`=`231`
`154+2pir^2`=`231`
`2pir^2`=`77`
`r`=`sqrt77//2pi`
volume of the cyclinder=`pir^2h`
We have given that
`2pirh`=`2//3(2pirh+2pir^2)`
therefore,`h`=`2r`
Volume=`pir^2xx2r`
=`2pir^3`
=`2pixx(77//2pi))3/2`
=`77xxsqrt77//2pi`
Hence, the volume of the cyclinder=`77sqrt77//2picm^3`