Question

A zoo is creating a new exhibit that includes an aquarium in the shape of a right rectangular prism. The water level of the aquarium is 2/3 the height of the aquarium as shown. How much space, in cubic feet, in the aquarium does not contain water?

Answer 1

`Volume=56(1)/(4)` cubic feet

Explanation:

Given

`L =3(3)/(8)ft` --- Length

`W =13(1)/(3)ft` --- Width

`H =3(3)/(4)` --- Tank

`Water\ level = (2)/(3)`

Required

Space not covered with water

If the water level is:

`Water\ level = (2)/(3)`

Then the empty space is:

`Empty = 1 - Water\ level` --- Complement rule

`Empty = 1 - (2)/(3)`

Take LCM

`Empty = (3-2)/(3)`

`Empty = (1)/(3)`

So, the volume of the empty space is:

`Volume=L*W*H*Empty`

`Volume=3(3)/(8) *13(1)/(3)*3(3)/(4)*(1)/(3)`

Express fraction as improper fraction

`Volume=(27)/(8) *(40)/(3)*(15)/(4)*(1)/(3)`

Simplify

`Volume=(9)/(8) *(40)/(3)*(15)/(4)`

Simplify

`Volume=(3)/(8) *(40)/(1)*(15)/(4)`

Simplify

`Volume=(3)/(1) *(5)/(1)*(15)/(4)`

`Volume=(3*5*15)/(4)`

`Volume=(225)/(4)`

`Volume=56(1)/(4)`