Question

a factory makes aquariums. each aquarium is in the shape of a triangular prism, as shown below. if the factory makes 552 such aquariums, how much water will be needed to fill all of them (in cubic feet)?

Explanation:

Step1: Calculate the volume of one aquarium

The formula for the volume \(V\) of a triangular prism is \(V = B\times h\), where \(B\) is the area of the triangular base and \(h\) is the height (length) of the prism.
The area of the triangular base \(B=\frac{1}{2}\times base\times height\). Here, the base of the triangle is \(2\) ft and the height of the triangle (altitude) is \(3\) ft. So \(B = \frac{1}{2}\times2\times3= 3\) square - feet.
The length (height of the prism) \(h = 8\) ft.
Then the volume of one aquarium \(V=B\times h=3\times8 = 24\) cubic - feet.

Step2: Calculate the total volume of 552 aquariums

If there are \(n = 552\) aquariums, and the volume of one aquarium is \(V_1=24\) cubic - feet, then the total volume \(V_{total}=n\times V_1\).
\(V_{total}=552\times24=(500 + 50+2)\times24=500\times24+50\times24 + 2\times24\)
\(=12000+1200 + 48=13248\) cubic - feet.

Answer:

\(13248\) cubic - feet.