Question

A cubical tank has a volume of 8000 $m^3$. What is the height of the tank (in cm)? ___

Answer 1

Volume of cube = $a^3$, where a is the side length of the cube.

In any cube, length, breadth and height are all equal. So, the dimension of the cubical tank can be found by finding cube root of 8000.
$\begin{array}{cc}2& 8000\\ 2& 4000\\ 2& 2000\\ 2& 1000\\ 2& 500\\ 2& 250\\ 5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array}$

Prime factorisation of 8000 = 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$5 $\times$ 5 $\times$ 5

$\sqrt[3]{38000m^3}$ = $\sqrt[3]{3(2^3\times 2^3\times 5^3)m^3}$ = 20 m

Hence, height of tank = 20 $\times$ 100 = 2000 cm