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Question
A rectangular tank 15m long and 11m broad is required to receive entire liquid contents from a full cylindrical tank of internal diameter 21m and length 5m. Find least height of tank that will serve purpose .
Solution
Given length of rectangular tank = 15m
Breath of rectangular tank = 11m
Let height of rectangular tank be h
Volumeof rec tan gular tan k = lbh
Volume = 15 x 11 x h ____(1)
Given radius of cylindrical tank (r) =`21/2m`
Length/height of tank = 5m
Volume of cylindrical tan k = πr2h
`=pi(21/2)^2xx5` _______(2)
Since volumes are equal
Equating (1) and (2)
`15xx11xxh=pi(21/2)^2xx5`
⇒ `h=(22/7xx(21/2)^2xx5)/(15xx11)`
⇒ h = 10.5m
∴ Height of tank = 10.5m
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