Question

the dimensions of an aquarium are shown. how much water, in cubic feet, can we fill the aquarium with? the aquarium is a rectangular prism with length 2 ft, width \\(\frac{2}{3}\\) ft, height \\(1\frac{2}{5}\\) ft.

Explanation:

Step1: Recall the volume formula for a rectangular prism

The volume \( V \) of a rectangular prism (which the aquarium is) is given by \( V = l \times w \times h \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

Step2: Convert the mixed number to an improper fraction

The height is \( 1\frac{2}{5} \) ft. To convert this mixed number to an improper fraction, we use the formula \( a\frac{b}{c}=\frac{a\times c + b}{c} \). So, \( 1\frac{2}{5}=\frac{1\times5 + 2}{5}=\frac{7}{5} \) ft.

Step3: Multiply the length, width, and height

The length \( l = 2 \) ft, the width \( w=\frac{2}{3} \) ft, and the height \( h = \frac{7}{5} \) ft. Now we calculate the volume:

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Answer:

\( 1\frac{13}{15} \) cubic feet (or \( \frac{28}{15} \) cubic feet)