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 .

Answer 1

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