Question

A storage tank is in the form of a cube. When it is full of water, the volume of water is $15.625m^3$. If the present depth of water is $1.3m,$ find the volume of water already used from the tank.

Answer 1

Step 1: Find the length of the edge of cube

Given,

The volume of water$=15.625m^3$

The present depth of the water is $1.3m$

Find out

We have to determine the volume of water already used from the tank.

Solution

When the cubical tank is full:

Volume of water $=$ Volume of cube $=15.625m^3$

So,

The volume of cube = (length of the edge of cube)³

⇒ (length of the edge of cube)${}^3=15.625$

⇒ length of the edge of cube $=∛15.625=2.5m$

When the present depth of the water is $1.3m$

Step 2: Find the volume of water already used

Length of tank $=2.5m$

Breadth of tank$=2.5m$

So, volume of water upto $1.3m$ $depth=length\times breadth\times depth$

$$\begin{gathered} =2.5\times 2.5\times 1.3 \\ =8.125m^3 \end{gathered}$$

Then, the volume of water already used from the tank

$=(Volumeof\tan kwhenitwasfullofwater)–(Volumeofwaterwhendepthis1.3m)$

$$\begin{gathered} =15.625–8.125 \\ =7.5m^3 \end{gathered}$$

Thus, the volume of water already used from the tank is $7.5m^3$.