Question

If a cubical tank has a volume of $27000m^3$, then the height of the tank is _____m.

• A. 15
• B. 20
• C. 25
• D. 30

Answer 1

The correct option is D 30

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 27000.
$\begin{array}{cc}2& 27000\\ 2& 13500\\ 2& 6750\\ 3& 3375\\ 3& 1125\\ 3& 375\\ 5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array}$
$\Rightarrow$27000 = 2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 3 $\times$ 3 $\times$5 $\times$ 5 $\times$ 5
$\sqrt[3]{327000m^3}$ = $\sqrt[3]{3(2^3\times 3^3\times 5^3)m^3}$
= 2 x 3 x 5 m
= 30 m
$\therefore$ The height of the tank is 30 m.