If the surface area of a right circular cylindrical pillar is 264 sq-metres and volume is 396 cubic-metres, then calculate height and length of diameter of this pillar.

Explanation

Let the height and radius of the pillar be h metres and r metres respectively.
`:.` the surface area of the pillar`=2xx(22)/(7)xxr xx h` sq. metres `= (44)/(7) ` rh sq.meters
As per question, `(44)/(7) rh = 264 ` or, `rh=(264xx7)/(44)=42` ..........(1)
Again, volumed of the pillar `= (22)/(7) xx r^(2) xx h ` cubic.metres
As per question, `(22)/(7) r^(2)h = 396` or, `(22)/(7) xx rh xx r= 396` or,`(22)/(7) xx 42 xx r = 396` [ from (1) ]
or, ` r = (396)/(22xx6)=3 :. 2r = 2 xx 3 = 6 . :.h=(42)/(3)=14`.
Hence the required height `= 14 cm` and length of diameter `= 6cm`