Question

The water from a cylindrical tank of height 12 m and diameter of base 7 m is emptied into two small cubic tanks of equal capacity. The length of the edge of the tank is 7 m. If one tank is completely filled, find the height of water in the second tank.

Answer 1

Given that height of the cylinder h = 12 m

Given that diameter of the cylinder d = 7 m

we know that radius r = d/2 = 7/2 = 3.5 m

volume of cylindrical tank is given by

$V=\pi r^2h$

$V=3.14 *3.5^2*12 = 461.58$ cubic metres

Given that side length of the cubical tank = 7 m

We know that volume of cubical tanks is given by

$V=x^3$  where x is the side length of the cube

$V=7^3 = 343$

Other cubical box has also same side length 7 m but the height of water is unknown so let it be x metre.

then volume of the other cubical tank = 7*7*x= 49x

Given that water from cylindrical tank is poured into other two cubical tanks then volume of water in cylinrical tank will be equal to sum of volume of water in both cubical tanks

49x + 343 = 461.58

49x = 461.58 - 343

49x = 118.58

x = 2.42

Hence final answer is 2.42 metres.