The curved surface area and the volume of a pillar are `264 m^(2) and 396 m^(3)` respectively. Find the diameter and the height of the pillar.

Explanation

Let the radius of the pillar be `r` metres and its height be `h` metres. Then,
`2pirh = 264` ...(i)
and `pi r^(2) h = 396` ....(ii)
On dividing (ii) by (i), we get
`(pi r^(2)h)/(2pirh) = (396)/(264) rArr r = ((2 xx 396)/(264)) = 3 rArr 2r = 6`
Hence, the diameter of the pillar is `6m`
Putting `r = 3` in (i), we get
`2 xx (22)/(7) xx 3 xx h = 264 rArr h = (264 xx (7)/(132)) = 14`
Hence, the height of the pillar is `14 m.`