Question

A rectangular tank 158 m long and 11 m broad is required to receive entire liquid contents from a full 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

Length of the rectangular tank = 15 m
Breadth of the rectangular tank = 11 m
Let the height of the tank after the liquid be 'h' m

Volume of the liquid in the rectangular tank = 15 x 11 x h

Diameter of the cylindrical tank = 21 m
Radius of the cylindrical tank = (21 / 2) m
Length or height = 5 m

Volume of the cylindrical tank = $\pi r^{2}h$
= 22/7 x 21/2 x 21/2 x 5
⇒ 15 x 11 x h = 22/7 x 21/2 x 21/2 x 5
⇒ h = 22/7 x 21/2 x 21/2 x 5 x 1/15 x 1/11
⇒ h = 21/2
⇒ h = 10.5 m