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The volume of a cylindrical vessel is 27...

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

Text Solution

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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
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