Question

A cubical tank is filled with water upto 2m below actual level. If the volume of water is 245m^3. Find the length, breadth and height of the tank.​

Answer 1

Answer:

The length, breadth, and height of the cubical tank are 7 meters each.

Step-by-step explanation:

A cubical tank has equal length breadth and height. Let this measurement be $x$. Since the water  level is 2 meters below the actual height, the height to which the water is filled is $x-2$.

Also, we know that the volume of a cuboid is

$Volume = height\times length\times breadth$

Here the volume of water is $245m^3$.

Thus we have the equation,

$\implies x\times x\times (x-2)=245\\\\\implies x^2(x-2)=245\\\\\implies x^3-2x^2-245=0$

We need to solve this cubic equation.

The equation can be factorized as

$(x-7)(x^2+5x+35)=0$

The quadratic part has only complex solutions. Thus the value of $x$ is 7.

Hence the length, breadth, and height of the cubical tank is 7 meters each