Question

A storage tank in the form of a cube has water up to its brim. The amount of water in the tank is 4096 m³. After sometime some water was used and , it is found that the depth of water present is 12 m. Find the volume of water used.

• A. $1024{\text{m}}^3$
• B. $848{\text{m}}^3$
• C. $1184{\text{m}}^3$
• D. $988{\text{m}}^3$

Answer 1

The correct option is A

$1024{\text{m}}^3$

The storage tank is a cube of volume $4096{\text{m}}^3$
Let Side of cube = $a\text{m}$

Volume of cube, $a^3=4096a=\sqrt[3]{34096}=\sqrt[3]{316\times 16\times 16}\therefore a=16\text{m}$

The present depth of water = 12 m.

$\therefore$ Depth of water already used, $h^{{}^{\prime }}=16-12=4\text{m}$

$\therefore$ Volume of water used = $a\times a\times h^{{}^{\prime }}=16\times 16\times 4=1024{\text{m}}^3$