# A rectangular tank 15 m long and 11 m broad is required

Question:

A rectangular tank 15 m long and 11 m broad is required to receive entire liquid contents from a fully cylindrical tank of internal diameter 21 m and length 5 m. Find the least height of the tank that will serve the purpose.

Solution:

Suppose height of the rectangular tank is equal to h.

Length of the tank = 15 m

Breadth of the tank = 11 m

Further,

length of cylindrical tank = 5 m

Radius of cylindrical tank $=\frac{21}{2} \mathrm{~m}$

To find out the least height of the tank, equate the volumes of two tanks.

$15 \times 11 \times h=\pi\left(\frac{21}{2}\right)^{2} \times 5$

$\Rightarrow h=\frac{22}{7} \times \frac{21}{2} \times \frac{21}{2} \times \frac{5}{15} \times \frac{1}{11}$

$\Rightarrow h=\frac{21}{2}$

$\Rightarrow h=10.5$

Hence, the least height of the tank is equal to 10.5.