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.

Answer 1

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 = $\frac{21}{2}$m
To find out the least height of the tank, equate the volumes of two tanks.
$$\begin{gathered} 15\times 11\times h=\mathrm{\pi }{\left(\frac{21}{2}\right)}^2\times 5 \\ \Rightarrow h=\frac{22}{7}\times \frac{21}{2}\times \frac{21}{2}\times \frac{5}{15}\times \frac{1}{11} \\ \Rightarrow h=\frac{21}{2} \\ \Rightarrow h=10.5 \end{gathered}$$
Hence, the least height of the tank is equal to 10.5.