The volume of the tank is the amount of water that can fill it.
The volume of the tank that needs to be filled in is [tex]66\frac {2}3[/tex]
How to determine the volume to fill in
The height of the tank is:
[tex]H =3[/tex]
The height of the water in the tank is:
[tex]h =\frac 13[/tex]
So, the height (x) of the empty space is calculated as:
[tex]x = 3 -\frac 13[/tex]
Evaluate the difference
[tex]x = \frac 83[/tex]
The volume of water to fill in, is then calculated as:
[tex]V = L * W * x[/tex]
This gives
[tex]V = 5 * 1\frac 23 * \frac 83[/tex]
Rewrite as:
[tex]V = 5 * \frac 53 * \frac 83[/tex]
Evaluate the product
[tex]V = \frac {200}3[/tex]
Rewrite as:
[tex]V =66\frac {2}3[/tex]
Hence, the volume of the tank that needs to be filled in is [tex]66\frac {2}3[/tex]
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