The volume of a cylindrical vessel is `27720 cm^(3)`. Itscurved surface is `2640 cm^(2)`. Find its height and radius of base.

Explanation

Let the height of the cylindrical vessel be `h` and radius be `r`
`therefore` Curved surface area `= 2pi rh = 2640`
`rArr pi rh=(2640)/(2)`
`rArr pi rh = 1320`
and volume `= pi r^(2)h=27720`
`rArr r(pi rh)=27720`
`rArr r xx 1320 = 27720`
`rArr r = (27720)/(1320)=21`
Put r = 21 in eq. (1),
`(22)/(7)xx21xxh=1320`
`rArr h=(1320)/(22xx3)=20`
`therefore` Height `= 20 cm` and radius `= 21 cm.`