Answer:
[tex]Volume=56\frac{1}{4}[/tex] cubic feet
Step-by-step explanation:
Given
[tex]L =3\frac{3}{8}ft[/tex] --- Length
[tex]W =13\frac{1}{3}ft[/tex] --- Width
[tex]H =3\frac{3}{4}[/tex] --- Tank
[tex]Water\ level = \frac{2}{3}[/tex]
Required
Space not covered with water
If the water level is:
[tex]Water\ level = \frac{2}{3}[/tex]
Then the empty space is:
[tex]Empty = 1 - Water\ level[/tex] --- Complement rule
[tex]Empty = 1 - \frac{2}{3}[/tex]
Take LCM
[tex]Empty = \frac{3-2}{3}[/tex]
[tex]Empty = \frac{1}{3}[/tex]
So, the volume of the empty space is:
[tex]Volume=L*W*H*Empty[/tex]
[tex]Volume=3\frac{3}{8} *13\frac{1}{3}*3\frac{3}{4}*\frac{1}{3}[/tex]
Express fraction as improper fraction
[tex]Volume=\frac{27}{8} *\frac{40}{3}*\frac{15}{4}*\frac{1}{3}[/tex]
Simplify
[tex]Volume=\frac{9}{8} *\frac{40}{3}*\frac{15}{4}[/tex]
Simplify
[tex]Volume=\frac{3}{8} *\frac{40}{1}*\frac{15}{4}[/tex]
Simplify
[tex]Volume=\frac{3}{1} *\frac{5}{1}*\frac{15}{4}[/tex]
[tex]Volume=\frac{3*5*15}{4}[/tex]
[tex]Volume=\frac{225}{4}[/tex]
[tex]Volume=56\frac{1}{4}[/tex]
