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

Answer:

$Volume=56\frac{1}{4}$ cubic feet

Step-by-step explanation:

Given

$L =3\frac{3}{8}ft$ --- Length

$W =13\frac{1}{3}ft$ --- Width

$H =3\frac{3}{4}$ --- Tank

$Water\ level = \frac{2}{3}$

Required

Space not covered with water

If the water level is:

$Water\ level = \frac{2}{3}$

Then the empty space is:

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

$Empty = 1 - \frac{2}{3}$

Take LCM

$Empty = \frac{3-2}{3}$

$Empty = \frac{1}{3}$

So, the volume of the empty space is:

$Volume=L*W*H*Empty$

$Volume=3\frac{3}{8} *13\frac{1}{3}*3\frac{3}{4}*\frac{1}{3}$

Express fraction as improper fraction

$Volume=\frac{27}{8} *\frac{40}{3}*\frac{15}{4}*\frac{1}{3}$

Simplify

$Volume=\frac{9}{8} *\frac{40}{3}*\frac{15}{4}$

Simplify

$Volume=\frac{3}{8} *\frac{40}{1}*\frac{15}{4}$

Simplify

$Volume=\frac{3}{1} *\frac{5}{1}*\frac{15}{4}$

$Volume=\frac{3*5*15}{4}$

$Volume=\frac{225}{4}$

$Volume=56\frac{1}{4}$