Question

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?

Answer 1

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

Answer 2

36 Quarts

Explanation:

Let the volume of the Aquarium be x quarts.

Hence amount of water filled in it will be

`(2x)/(3)` 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

`(x)/(2)`

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

`(2x)/(3)-(x)/(2)=6`

`(4x-3x)/(6)=6`

`x=36`

Hence the volume of the tank is 36 quarts.