A rectangular aquarium is 2/3 filled with water and then is tilted on its side until the water level coincides with one edge of the bottom. During the process, 6 quarts of water are poured out. What is the volume of the tank in quarts?

let A, B, C be the dimensions of the rectangular aquarium. Volume = A x B x C 2/3 ABC - 6 = 1/2 ABC ABC((2/3)-(1/2)) = 6 Volume =ABC = 6 x 6 = 36 quarts

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Cricetus Cricetus · Answer 2 · 2019-07-27T10:20:46+02:00

Answer:

36 Quarts

Step-by-step explanation:

Let the volume of the Aquarium be x quarts.

Hence amount of water filled in it will be

[tex]\frac{2x}{3}[/tex] quarts

Also problem says that the tank is tilted until water level coincides with one edge of the bottom. At this position , the amount of water filled in the tank will be half of the total volume , as the slant water level will be the diagonal of the tank and a diagonal divides the tank in two halves.

Hence current volume of water in the tank will be

[tex]\frac{x}{2}[/tex]

And in this process the amount of water poured out is 6 quarts. It will the difference between the amount of water earlier in the tank and the amount of water in the tank now. Hence

[tex]\frac{2x}{3}-\frac{x}{2}=6[/tex]

[tex]\frac{4x-3x}{6}=6[/tex]

[tex]x=36[/tex]

Hence the volume of the tank is 36 quarts.